Math - Precalculus

In isosceles trapezoid HJKL, JK is parallel to HL. If m < L = 45°, JK = 6 cm, and the length of an altitude is 4 cm, find the exact perimeter of HJKL.

(20 + 8 square root of 2) cm

What is the measure of each indicated angle?

108°

Determine the number of sides of a polygon that has 44 diagonals.

11

For parallel lines a and b, <1 and <5 are corresponding angles. If m<1 = 5(x+3) and m<5 = 7(x-1), find x.

11 degrees

In triangle <RST, m<S = 84° and m<T = 42°. The bisectors of <R and <S meet at point V in the interior of Triangle <RST. What is the measure of <RVS?

112 degrees

Find the number of sides that a regular polygon has if the measure of each interior angle is 150°

12

Point P lies in the exterior of circle O so that PA is tangent to the circle. Also, PC is a secant that intersects circle O at B and C, where P-B-C. If PB = 9 and BC = 7, find PA.

12

ABCD and triangle XYZ have the same length of base and the same length of altitude.If the area of ABCD is 25 m^2, find the area of triangle XYZ.

12.5 in^2

A circle has the area 126 squared centimeters. To the nearest tenth of a centimeter, find the length of its diameter.

12.7 cm

In the circle, m arc CA= 95° and m arc AB = 60°. Where M is the midpoint of AB, find mCAM.

125°

Find the number of sides that a polygon has if the sum of the measures of its interior angles is 1980°.

13

Two angles are a linear pair. Their measures are represented by x+10, and 3x+10. What is the measures of the second angle?

130°

Find the measure of each interior angle of a regular octagon.

135°

Two angles are supplementary. If 2 times the measure of one angle is 6 times the measure of the other angle, determine the measure of the larger angle.

135°

What is the measure of each interior angle of a stop sign?

135°

Find the measure of each interior angle of a regular polygon of 10 sides

144°

What is the value of x in the figure

14°

In triangle RST, m<R = 37° and m<S = 116°. Find the measure of exterior angle RTV.

153 degrees

The diagonals of quadrilateral ABCD are perpendicular. If AC = 14 inches and BD = 25 inches, find the area of ABCD.

175 square inches

Find the total number of diagonals for a polygon of 8 sides.

20

The pentagon shown is composed of square ABCD and isosceles triangle BXC in which m < X = 90°. If AD = 4 cm, find the area of the pentagon.

20 square cm

Find the value of x if: m<1=x m<2=2x-10 m<3=2x+10

20°

Ray OB is the bisector of ∠AOC. The measure of ∠AOC = 7x+2 degrees and ∠ COB = 5x - 8 degrees. What is the measure of ∠ AOB?

22°

Given: Ray ST bisects ∠ RSV m∠ RST = x + y m∠ TSV = 2x - 2y m∠ RSV = 64° Find: x

24 degrees

If measure of a = x+28 and measure of b = 5x-4, determine the value of x.

26°

For the concentric circles, the outer circle radius is R = 6 in while that of the inner circle is r = 3 in. Find the exact area of the annulus (ring) that is determined by the two circles.

27 pi square units (?)

For circle P, radii PX and PY and arc XY bound a sector. If m XY = 100° and PX = 5.6 inches, find the area of the sector correct to the nearest tenth of a square inch.

27.4 square inches

In circle O, m < AOC = 58°. Find mABC.

29 degrees

In circle O, radius OD is perpendicular to chord AB at point C. If OD = 5 and AB = 8, find OC.

3

A square has an area of 13 square inches. What is the exact length of each side of the square?

3.6 inches

In the figure, secants AB and AC intersect the circle at points R and S respectively. If m < A = 30° and m arc BC : m arc RS = 3:1, find m arc RS.

30 degrees

Find the measure of each exterior angle of a regular polygon of 12 sides

30°

Two angles are complementary. The measure of one angle is twice the measure of the other. Determine the smaller angle.

30°

In triangle RST, <R is a right angle. If m<S is 26° larger than m<T, find m<T.

32°

In trapezoid RSTV, ST is parallel to RV. If SR = TV = 6 cm, ST = 4 cm, and m <R = 60°, find the area of RSTV.

36 square cm.

In MPQ, QR is perpendicular to MP. If MQ = 10, RP = 4, and MR = 8, find the area of MPQ.

36 square units

Find the are of the shaded region

36.5 square units

When two parallel lines are cut by a transversal, <1 and <5 are a pair of corresponding angles that are formed. If m<1 = 2(x-15) and m<5 = x/2 + 30, find x.

40 degrees

The supplement of an angle is twenty degrees less than four times the angle. Find the measure of the angle.

40°

Along a straight shoreline, two houses are located at points H and M. The houses are 5000 feet apart. A small island lies in view of both houses, with angles as indicated. Find m∠I.

44°

Given MN is perpendicular to NQ, and <S as shown, Find Y

44°

The exterior sides of adjacent angles 1 and 2 are perpendicular. If BD is the bisector of <1 and BE is the bisector of <2, find the measure of DBE

45 degrees

AB is tangent to circle O at point B. If m arc CB = 40°, find m <A.

50 degrees

In the circle, chords AB and CD intersect at point P. If m < APD = 60° and m or arc AD = 70°, find m of arc CB.

50 degrees

If m <B = 25°, find m <APC if BC is the diameter.

50°

With PT and PS both tangent to the circle as shown. If measure of arc ST = 130° find the measure of both < T and < S

50° (?)

Triangle ABC is a right triangle with ∠C being the right angle. ∠A is 7x + 4 and ∠B is 5x + 2. What is the angle measurement of ∠ A?

53°

Given: m∠ RST = 2x - 10 m∠ TSV = x + 6 m∠ RSV = 4(x - 6) Find: m∠ RSV

56°

Find the exact area of a triangle whose sides measure 5, 6, and 7.

6 square root of 6 units ^2

In circle P, radii PA and PB are congruent to chord AB. Find m< P.

60 degrees

For rectangle ABCD, AB = 5 inches while the length of a diagonal is AC = 13 inches. Find the area of the rectangle.

60 square inches

m∠ RST =x2 m∠ TSV =x4 m∠ RSV = 45° Find: x

60°

The number of diagonals D for a polygon of n sides is given by D=n(n-3)/2. Find the number of sides for a polygon that has 14 diagonals.

7

The area of RSTV is 35.1 cm^2. Choosing a side of RSTV that measures 4.5cm as the base, what is the length of the corresponding altitude?

7.8 cm

In the circle, m BC = 68° and m AD = 74°. Find m APD.

71 degrees

Find the sum of the measures of the interior angles of a polygon of 6 sides

720°

Solve for x, if ∠1 = (4x+40) and ∠2 = (6x-20)

7°

Find the length of the minor arc AB. Radius is 8 inches.

8.4 units

In triangle ABC, m<A= 4x, m<B= 3x, and m<C= 2x. find m<A.

80°

Points A, B, and C are collinear on horizontal line segment AC. Point D lies above AC. If m<ABD is 14° larger than m<DBC, find m<.DBC

83 degrees

Find the area of the triangle whose sides have lengths 13 cm, 14 cm, and 15 cm.

84 square cm

Find the total number of diagonals for a concave hexagon.

9

In circle P, a sector is bounded by radii PX and PY and arc XY. If m XY = 90° and PX = 6 m, find the exact area of the sector.

9 pi m ^2

Two parallel lines l and m are cut by transversal t. For a pair of interior angles on one side of line t, the angle-bisectors are drawn to meet at point E. Find m<E.

90°

If m arc CA = 100° and m AB = 70°, find the measure of CAB (not shown).

95°

Assuming that BG is perpendicular to CD and BH is perpendicular to AD in ABCD, what line segment is the altitude of this parallelogram with respect to side AB?

BG

Each interior angle of a regular hexagon measures 60°.

False

If RV is perpendicular to TW, then the altitude to base TV of rectangle RSTV is RW.

False

If m of arc AB= 75° in circle O, then m of arc ACB = 275°.

False

In the circle shown, mAB = mCD. Are these arcs congruent?

False

The area of the trapezoid with base lengths b1 and b2 and altitude h is given by A = h(b1 + b2).

False

The region bounded by radii OA and OB and arc AB is known as a secant of the circle.

False

The sum of the measures of the four interior angles of a quadrilateral is 270°.

False (Since the correct answer is 360°

To determine the measure of < A, which expression should be calculated? a) 1/2 (mRS - mBC) or b) 1/2 (mBC - mRS) ?

b)

Write the formula for the area A of any quadrilateral that has perpendicular diagonals of lengths d1 and d2.

half the product of the diagonals

With chords RS and TV intersecting in the interior of the circle, what expression can be used to find m RXV?

half the sum of measures of intercepted arcs RV and TS.

If <1 and <2 are not congruent, what conclusion can you draw about lines a and b?

lines a and b are not parallel

If r || s and m<1 = 108°, then:

m<2 = 72°

If m<1 = x and 90° < x < 180°, then m<1 is a(n):

obtuse angle

If <1 and <2 are supplementary and <1 is congruent to <2, then <1 must be a(n):

right angle

If two angles are supplementary and also congruent, then each of these angles is a(n):

right angle

The measures of the three interior angles of a triangle are x, 2x, and 3x. What type of triangle is the triangle described above based only on the angles?

right angle triangle

When two parallel lines are cut by a transversal, <3 and <6 are a pair of alternate interior angles formed. If m<3 = x^2 + 5x and m<6 = x(x-2), find x.

x = 7

If points C and B are the endpoints of diameter and A is any other point on circle O, find the measure of angle ACB.

None of These (45 degrees)

Find the sum of the interior angles of a hexagon. 360° 540° None of These 180°

None of These (Since the answer is 720°)

What does the letter D represent in the formula D=n(n-3)/2?

Number of diagonals of the polygon

If two parallel lines are cut by a transversal, then the interior angles on the same side of the transversal are:

Supplementary

In this figure, <1 and <2 are complementary. Also, <2 and <3 are complementary. Regarding <1 and <3, what conclusion may you draw?

The angles are equal

AB and CD intersect at point E. If <AEC is a right angle, what relationship exists between AB and CD?

They are perpendicular

Congruent circles have the same length of radius while concentric circles have the same center.

True

For a circle, the constant ratio of the circumference C to length of diameter d is represented by the number pi.

True

For an isosceles triangle with length of leg s and length of base b, the perimeter P is given by P = 2s + b.

True

For any quadrilateral with perpendicular diagonals of lengths d1 and d2, the area is given by A = 1/2 (d1)(d2)

True

Given that r || s and transversal t, ∠1 and ∠6 are supplementary.

True

If a triangle has exactly two congruent sides, then it is an isosceles triangle.

True

If both a parallelogram and triangle have the same base and altitude, then the area of the parallelogram is twice the area of the triangle.

True

In the figure, <RXT and <VXS are known as vertical angles.

True

The polygon shown is concave.

True

Where m AB = x and DA and DB are tangents to the circle, m<D = 180 - x

True

With the circle inscribed in triangle ABC, it follows that AR = AS, BS = BT, and CR = CT.

True