Parallel Lines/ Triangle Test
Answer: ∠J = 30°
Find the measure of angle J if the measure of angle A is 120 and J and C are congruent.
Answer: <1 & <4 <9 & <6
Identify a pair of corresponding angles in the diagram.
Answer: 32° Since a triangle has a total value of 180° when you add together all three angles, when you add 58° + 90° + x = 180°. Then solve the equation to determine the value of x to be 32°.
Using the diagram what is the m<C?
Answer: w=3 8w + 40 - 3w - 52 = 2w + 6 - 3w ← Combine like terms 5w - 12 = -w + 6 ← add 12 to both sides 5w = -w + 18 ← add w to both sides 6w = 18 ← divide both sides by 6 w = 3
Solve the following equation for w. 8w + 40 - 3w - 52 = 2w + 6 - 3w
Answer: m∠A = 120° it is vertical to ∠M m∠T = 25°, a triangle is equal to 180° so 35°+ x + 120 = 180°
Answer the following questions using the diagram below m<M = 120 m<A =______ m<T =______ m<H = 53
Answer: The new triangle should be flipped over the y- axis, this is the axis that runs from top to bottom. Here is and example of a symbol reflected over the y axis,
Draw a reflection of the triangle over the y-axis.
Answer: X = 10 m<J = 58° m<E = 44° m<N= 78°
Find the value of x and then find the value of each angle. X = _______ m<J = _________ m<E = _________ m<N=__________
Answer: 85° The exterior angle has a value of 145, and we know that the combined value of the remote interior angles must equal the value of the exterior angle (145). We are told that one of the remote interior angles has a value of 60 and we do not know the value of the other remote interior angle. We can now write an equation using x to solve for the unknown value of <F. 60° + X = 145° X = 85°
Find ∠F
Answer: Line a is not parallel to line b. We know this because the identified angles are alternate interior angles, and when you have parallel lines the alternate interior angles are congruent, which means equal. However, the angle values of 41 and 42 are not congruent; therefore lines a & b are not parallel.
For the figure shown, decide if line a is parallel to line b. Justify your reasoning.
Answer: ∠1 & ∠5 ∠8 & ∠4 Remember - exterior means outside the parallel lines and alternate means the opposite side for the transversal
Identify the alternate exterior angles, and explain how they could be used to prove line a and line b are parallel.
Answer: ∠2 & ∠6 ∠7 & ∠3 Remember - interior means inside the parallel lines and alternate means opposite sides of the transversal
Identify the alternate interior angles, and explain how they could be used to prove line a and line b are parallel.
Answer ∠1 & ∠3 ∠8 & ∠6 ∠2 & ∠4 ∠7 & ∠5 Remember - corresponding angles are when you cut a line and either slide it up and down or left and right to place it over the line it ran parallel to. The corresponding angles are those angles that over lap.
Identify the corresponding angles, and explain how they could be used to prove line a and line b are parallel.
Answer: 130° The measure of angle x must be 130 since the 50 angle has an alternate exterior angle that is supplementary to angle x. This means that the alternate exterior angle for the 50 angle is the angle just above x. Since the angle above x is 50, and they are adjacent to one another they are supplementary angles. Supplementary angles have a combine value of 180 degrees. 50° + x = 180° x=130°
In the diagram below, line m, intersects line a and line c. What does the measure of x have to be for line a and line c to be parallel
Answer: m<4 = 140° <7 is supplementary to <5, which means when you add together the m<7 and m<5 is should equal 180°. Since <5 is then 140°, so too, should be m<4 since <4 & <5 are alternate interior angles as long as line a is parallel to line m then the angles should be congruent.
In the diagram below, line t intersects line a and line m. If the m<7 = 40, what does the measure of <4 have to be for line a to be parallel to line m?
Answer ∠ECK = 72° because it creates a straight line with ∠ECF & ∠KCB. Since the three angles share the same point on a straight line their total value is 180°. Therefore 38° + 70° + x = 180°. The value of the unknown angle will be 72°. ∠BCG = 38° it is vertical to ∠ECF, which makes them congruent ∠GCW = 72° it is vertical to ∠KCE, which makes them congruent ∠WCF = 70° it is vertical to ∠KCB, which makes them congruent
In the diagram below, three lines intersect at C. The measure of <KCB is 70 and the measure of <ECF is 38. Label all the remaining angles in the picture with the correct measures.
Answer x = 20 Since a straight line equals 180 degrees 5x + 13 + 3x + 7 = 180 8x + 20 = 180 8x = 160 x= 20
In the diagram line W and line F are parallel. Solve for x.
Answer: ∠1 = 132° ∠2 = 48°
Is ∆JAC ∼∆PAT? Justify your answer. What is the measure of ∠1 and ∠2? (Note ∠TAP = 42°, The m∠ATP is unknown)
Answer: x²y/5 Since the bases are the same you will subtract the exponents. When you divide 2 by 10 you will get 1/5. Then subtract 3 - 1, you will get a solution of 2 which will be the exponent value for the base of x. Now 4 -3, will give you the exponent value of 1 for y, which does not need to be written since 1 is assumed when not stated.
Simplify the expression
Answer: ∠e = 115° it is alternate interior angle to ∠115° ∠c = 65° it is supplementary to ∠115° ∠f = 65° it is supplementary to ∠e ∠h = 115° it is corresponding to ∠115°
The figure below shows parallel lines cut by a transversal. What is the measure of <e? Why What is the measure of <c? Why What is the measure of <f? Why What is the measure of <h? Why
Answer: 91° Since the total degree value of a triangle is 180 degrees. You will need to add all the known angle values together and then subtract that value from 180 to determine the value of the missing angle. 37° + 52° + x = 180° 89° + x = 180° x = 91°
Using the diagram, what is the measure of angle P?
Answer: ∠3 & ∠5 To find the remote interior angle when compared to ∠1 you will look inside, the interior, of the triangle and select the two angles that are the furthest away from ∠1. The two interior angles that are furthest away from ∠1 are angles ∠3 & ∠5.
What are the two remote interior angles for ∠1?
Answer: 72° Because ∠2 is an exterior angle and we know that when you add together the value of 2 remote interior angles you will get the value of the exterior angle. 30° + 42° = 72°
What is the value of ∠2?
Answer: ∆JKL & ∆MNP To determine which ∆'s are similar you need to determine the value of the unknown angles you will need to add the two known angles of each triangle together and then subtract that value from 180 (which is the total angle value for a triangle) to determine the value of the missing angle ∆JKL 62 +58 +K = 180 K = 60 ∆MNP 60 + 58 + P = 180 P = 62 ∆QRS Q + 64 + 58 = 180 Q = 58
Which triangles are similar?
Answer: 8.4 × 10⁻⁴ To have a number in scientific notation the first factor must have a value greater or equal to one and less than 10. Your second factor will be 10 with an exponent indicating if the value of the original number is less than one or greater than one. Since the original number has a value of less than one the exponent will be negative. Your exponent value will be -4, since you will have to move the decimal in the number 8.4 four spaces to the left in order to get the original value
Write 0.00084 in scientific notation.
Answer: ∠X + ∠Y + ∠Z = 180° When you combine all the angles of a triangle the total is always 180 degrees; therefore, you will add angle X plus angle Y plus angle Z to get the total value of 180°
Write an equation to solve for the measure of each angle in ∆ XYZ?