Geometry

Find the value of x. An octagon is drawn. The first angle measure is 6x degrees. The second angle measure is 102 degrees. The third angle measure is 132 degrees. The fourth angle measure is 132 degrees. The fifth angle measure is 6x degrees. The sixth angle measure is 124 degrees. The seventh angle measure is 140 degrees. The eighth angle measure is 119 degrees.

About 27.6

Exterior angles

Always sum up to 360

Find BC. Triangle ABC is drawn with a line AD running through the middle. Line AD creates two triangles. Triangle ACD is a right triangle, line AC has a measure of 24. Triangle ABD side line AB has a measure of 24 and a base measure of 15.

BC = 30

In the diagram, Find BD . Three rays are drawn. Ray B, ray D and ray C all intersect at point A. Ray B and D make a right triangle and the base has a measure of 6x + 3. Ray D and C make a right triangle and the base has a measure of 3x + 6.

BD = 9

Find the coordinates of vertex C for the figure placed in a coordinate plane. an isosceles triangle Triangle ABC is drawn in a coordinate plane along an X and Y axis. The vertexes for each point: A (0, 0), B (3, 6), and C vertexes is not given.

C(6,0)

List the sides of ABC from shortest to longest. Triangle ABC is drawn and angle measures are given. The angle measure of A is 57 degrees. The angle measure of B is 63 degrees. The angle measure of C is 60 degrees.

CB, AB, AC

A stop sign is shaped like a regular octagon. Find the measure of each interior angle of the stop sign. Then find the measure of each exterior angle.

Interior: 135, exterior: 45

Classify the indicated triangular shape of the stained glass window in the diagram by its sides and by measuring its angles. Image drawn is of a triangle with two congruent sides and has one wide angle.

Isosceles obtuse

In the diagram, M is the midpoint of ABC. Find the coordinates of M. Triangle ABC is drawn on a graph with an X and Y axis each go up by the count of 2s and end at 6. Point A (0, 0), point B (0, 4), and point C (3, 0). Line BC has a midpoint

M (3/2, 2).

You and your brother are going different places for the holiday, but you make the 25-mile drive due north to the airport together. You fly 225 miles 15° toward west to reach your destination, while your brother flies 225 miles 25° toward east to reach his destination. Who is farther from home?

Me

Are the triangles congruent by the ASA Congruence Theorem? Two triangles are drawn. The left side of each triangle are congruent. The middle angle of both triangles are congruent. The right side of each triangle are congruent.

No

Can the triangles be proven congruent with the information given in the diagram? If so, state the theorem you would use. Two triangles are drawn on a banner. The top angles are congruent and the bases are congruent.

No

In the diagram, mQS and mPR bisect each other at point T. Find the measure of mP. In the diagram line QS and line PR bisect each other at point T. This bisect creates two triangles. Triangle TRS and triangle TQP. The angle measure given for R is 2x degrees. The angle measure given for P is (x + 48) degrees.

P = 96

Write a congruence statement for the triangles. There are two triangles drawn. Triangle QRP and UTV. Points Q and U are congruent. Points R and T are congruent. Points P and V are congruent.

QRP = UTV

Interior angles

Sum up to 180 * the number of triangles the shape contains

A salt lick is 80 yards due north of your position. Two deer approach the salt lick, both 85 yards away from you. From your position, the buck is 45° west and the doe is 35° east. Which deer is farther from the salt lick?

The buck

A rectangular sheet of metal has a length of 40 inches and is cut along a diagonal to form two triangular pieces. One of the triangles has a leg length of 12 inches. Which statement is true?

The other triangle has a leg length of 12 inches

A railway turntable is used to turn locomotives around or quickly change their direction in small spaces. A locomotive enters the turntable on track 2, is rotated 180° counterclockwise, and exits the turntable. Which track does the train leave on?

Track 2

Find the values of x and y in the parallelogram when AB = x2 - 18, CD = 7x, D = 5y + 31, and B = 96

X = 9, Y = 13

In the diagram, mCDE = GHI. Find the value of y. Two scalene triangles are drawn. The first triangle is labeled CDE. Angle measure of point E is 62 degrees and point D is 65 degrees. Line CD of the triangle has a line measure of 11 cm. The second triangle is labeled GHI. Angle measure of point G is x degrees. Line GH of the triangle has a line measure of (x - y) cm.

Y = 42

Can the triangles be proven congruent with the information given in the diagram? If so, state the theorem you would use. Two triangles are drawn. A pair of angles and a pair of non-included sides are congruent.

Yes

In the diagram of the airplane below, can you use the Hypotenuse-Leg Congruence Theorem to prove that the triangles are congruent?

Yes

The pill container shown is shaped like a regular heptagon. Find the measure of each interior angle of the container. Then find the measure of each exterior angle. Round decimal answers to the nearest tenth of a degree.

interior: 128.6 °; exterior: 51.4 °

The badge shown is shaped like a regular nonagon. Find the measure of each interior angle of the badge. Then find the measure of each exterior angle.

interior: 140 °; exterior: 40 °

A surveyor uses the triangles shown in the diagram to measure the distance across a pond. What is the distance across the pond? Two triangles are drawn and the top points of each triangle are touching. The top triangle's right side has a measure of 41 ft. and the left side has a measure of 29 ft. The bottom triangle's right side has a measure of 29 ft. and the left side has a measure of 41 ft. The base of the bottom triangle has a measure of 52 ft.

52 ft

Find C when quadrilateral ABCD is a parallelogram

57

Find the sum of the measures of the interior angles of a convex hexagon.

720

Find the sum of the measures of the interior angles of the given figure. A hexagon is drawn.

720

Complete the statement 1 _ 2 with <, >, or =. Two triangles are drawn and a line runs through the center of these triangles connecting them together. Triangle 1 has a base measure of 27 and a side measure of 37. Triangle 2 has a base measure of 26 and a side measure of 37.

<

Complete the statement 1_2 with <, >, or =. Two triangles are drawn. Triangle 1 has a base measure of 18. Triangle 2 has a base measure of 19. Triangle One's two sides are congruent to triangle two's sides.

<

Graph AB with endpoints A (3, -3) and B (3, 1) and it's image after a reflection in the line Y = X.

A (-3, 3) and B (1, 3)

Find AB. Triangle ABC is drawn with a line AD running through the middle. Line AD creates two triangles. Triangle ACD is a right triangle, line AC has a measure of 5x - 6, and the base of the triangle is congruent to triangle ABD. Triangle ABD side line AB has a measure of 4x + 6.

AB = 54

List the sides of ABC from shortest to longest. Triangle ABC is drawn and angle measures are given. The angle measure of A is 63 degrees. The angle measure of B is 60 degrees.

AB, AC, CB

In LMN, point P is the centroid, and AN=18. Find AP and NP. Triangle LMN has a centroid point P. There is a line running through the triangle to create line segment AN, which has a measure of 18. Line segment AN can be divide into line segment AP and line segment NP.

AP = 6, NP = 12

In mLMN, point P is the centroid, and NP=14. Find AP and AN . Triangle LMN has a centroid point P. There is a line running through the triangle to create line segment AN. Line segment can be divide into line segment AP and line segment NP which has a measure length of 14.

AP = 7, AN = 21

Find the coordinates of the circumcenter of mABC with vertices A(-5,6), B(-7,2), and C(-3,2)

(-5, 3.5)

Find the coordinates of the circumcenter of mABC with vertices A(-4,0), B(8,3), and C(4,3).

(6, -14.5)

180 degree rotation

(X, Y) → (-X, -Y)

270 degree rotation

(X, Y) → (-Y, X)

The logo for a business is moved across a page 6 units right and 6 units down. Next, it is moved 2 units left and 2 units up. Rewrite the composition as a single translation.

(X, Y) → (X - 4, Y + 4)

90 Degree Rotation

(X, Y) → (Y, -X)

Find mKMN Triangle LKM is drawn and includes an auxiliary line starting at point M. This line is labeled MN. This line also creates an exterior angle labeled KMN. Point L on the triangle has a measure of 81 degrees. Point K on the triangle has a measure of 46 degrees. The exterior angle KMN has a measure of (13x + 36) degrees.

101

A convex pentagon has exterior angles of 83°, 83°, 26°, and 46°. What is the measure of an exterior angle at the fifth vertex?

122 degrees

Find mCAD. Three rays are drawn. Ray B, ray D and ray C all intersect at point A. Ray B and D make a right triangle BAD, and angle A has a measure of (3x + 7) degrees. Ray D and C make a right triangle, and has an angle measure of (10x - 7) degrees.

13 degrees

Find the value of x. A diamond, a quadrilateral, is drawn. The left corner angle's measure is 135 degrees. The top angle's measure is 68 degrees. The right corner angle's measure is 110 degrees. The bottom angle's measure is X degrees.

47

The Park and Recreation department wants to add some sidewalks to the park. The fountain F is located at the park's centroid and is 85 feet from entrance A. How many feet of sidewalk are needed to connect the fountain to the gift shop? A triangle is drawn and has a midpoint of F which represents the fountain of the park. Each point of the triangle is given a name petting zoo, gift shop, and snack cart. There is a line that goes through the middle of the triangle and through the midpoint of F. From the center point F and the entrance of the park, midpoint A, which is between the petting zoo and snack cart, this line has a measure of 85 feet. The center point f also connects to the point gift shop.

170 ft.

You install fencing around your large triangular garden. Then, you divide it into four small triangular gardens by connecting the midpoints of each side of the triangle with fencing. How many feet of fencing do you need? Triangle ABC is drawn and is divided into four small triangles. The left corner is labeled AGK. The top is labeled CKH. The middle is labeled KHG and side GH has a measure of 21 ft. The right corner is labeled GHB, and HB has a measure of 17 ft. and GB has a measure of 19 ft.

171 ft.

A road crew uses the triangles shown in the diagram to measure the width of a sink hole across a highway from a safe distance away. How wide is the sink hole? Two triangles are drawn and the top points of each triangle are touching. The top triangle's right side has a measure of 13 ft. and the left side has a measure of 15 ft. The bottom triangle's right side has a measure of 15 ft. and the left side has a measure of 15 ft. The base of the bottom triangle has a measure of 18 ft.

18 ft

How many lines of symmetry does a rhombus have?

2

Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement: A prism with 4 sides, tetrahedron, is drawn and the bottom of the prism is labeled to form line CP with a full measure of 10. From CP' the measure is 4.

2/5, reduction

Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement: A triangle is drawn and the bottom of the triangle is labeled to form line CP with a full measure of 15. From CP' the measure is 4.

2/5, reduction

Find mM. Two right triangles are drawn. The first triangle is labeled MNL and N has an angle measure of 90 degrees. The second triangle is labeled QRS and R has an angle measure of 90 degrees. S also has an angle measure of 70 degrees. Angles measures of S and L are marked as congruent angles.

20 degrees

A marine biologist uses the triangles shown in the diagram to measure the width of an oil spill in the bay from a safe distance on shore. How wide is the oil spill? Two triangles are drawn and the top points of each triangle are touching. The top triangle's right side has a measure of 17 m and the left side has a measure of 10 m. The bottom triangle's left side has a measure of 17 m and the right side has a measure of 10 m. The base of the bottom triangle has a measure of 20 m.

20m

A company builds trusses to support structures. In the truss shown below, the support mc016-1.jpg is the midsegment of mc016-2.jpg. Find the value of x. Triangle ABC is drawn and has a midsegment line which is labeled GH. This midsegment line creates a smaller triangle HGB and the base, which is labeled GB has a measurement of 21 ft. The midsegment line also creates a four sided shape GHCA, and the base of this shape, which is labeled AG has a measure of X ft.

21 ft.

Find mBAD. Three rays are drawn. Ray B, ray D and ray C all intersect at point A. Ray B and D make a right triangle and the base has a measure of 7. Ray D and C make a right triangle and the base has a measure of 7. Angle A of triangle DAC has a measure of 23 degrees.

23 degrees

An image of a celebrity is going to be used on a promotional billboard. This person is 6.25 feet tall in real life, and 21.875 feet tall on the billboard. What is the scale factor of this dilation

3.5

A parallelogram is formed by the supports that attach a basketball backboard and rim to the wall. The angles change as the basketball apparatus is taken out and put away. Find BCD when DAB = 32.

32