Question 1

The angle measures of a polygon with s sides is 3060. Find s.

Accepted Answer

19

Question 2

What is the measure of one angle in a regular 18-gon.

Accepted Answer

160

Question 3

Find the value of x. The diagram is not to scale.

Accepted Answer

45

Question 4

The sum of the measures of two exterior angles of a triangle is 256. What is the measure of the third exterior angle?

Accepted Answer

104

Question 5

Find the values of the variables in the parallelogram.

Accepted Answer

x=37, y=48, z=95

Answer

x=48, y=48, z=132

Answer

x=48, y=37, z=95

Answer

x=37, y=48, z=132

Question 6

In the parallelogram, m$\angle$QRP=64 and m$\angle$PRS=30. Find m$\angle$PQR.

Accepted Answer

86

Question 7

For the parallelogram, if m∠2 = 3x − 30 and m∠4 = 2x − 9, find m∠3. The diagram is not to scale.

Accepted Answer

147

Question 8

In parallelogram DEFG, DH = x + 3, HF = 2y, GH = 2x – 3, and HE = 3y + 1. Find the values of x and y. The diagram is not to scale.

Accepted Answer

x = 17, y = 10

Answer

x = 10, y = 17

Answer

x = 11, y = 19

Answer

x = 19, y = 11

Question 9

In the figure, the horizontal lines are parallel and AB = BC = CD. Find KL and FG. The diagram is not to scale.

Accepted Answer

KL = 8.2, FG = 7.8

Answer

KL = 8.2, FG = 8.2

Answer

KL = 7.8, FG = 7.8

Answer

KL = 7.8, FG = 8.2

Question 10

Find values of x and y for which ABCD must be a parallelogram. The diagram is not to scale.

Accepted Answer

x = 8, y = 3

Answer

x = 3, y = 8

Answer

x = 8, y = 11

Answer

x = 8, y = 24

Question 11

Classify the figure in as many ways as possible.

Question 12

In the rhombus, m∠1 = 15x, m∠2 = x + y, and m∠3 = 10z. Find the value of each variable. The diagram is not to scale.

Accepted Answer

x = 6, y = 84, z = 9

Answer

x = 12, y = 174, z = 9

Answer

x = 6, y = 174, z = 18

Answer

x = 12, y = 84, z = 18

Question 13

Find the measure of the numbered angles in the rhombus. The diagram is not to scale.

Accepted Answer

m∠1 = 90, m∠2 = 44, and m∠3 = 46

Answer

m∠1 = 90, m∠2 = 46, and m∠3 = 44

Answer

m∠1 = 90, m∠2 = 44, and m∠3 = 44

Answer

m∠1 = 90, m∠2 = 44, and m∠3 = 68

Question 14

In rectangle PQRS, PR = 20x – 19 and QS = x + 247. Find the value of x and the length of each diagonal.

Accepted Answer

x = 14, PR = 261, QS = 261

Answer

x = 7, PR = 254, QS = 254

Answer

x = 14, PR = 130.5, QS = 130.5

Answer

x = 15, PR = 281, QS = 281

Question 15

∠J and ∠M are base angles of isosceles trapezoid JKLM. If m∠J = 21x + 4, and m∠M = 14x + 11, find m∠K.

Accepted Answer

155

Question 16

$\overline{LM}$ is the midsegment of ABCD. AB = 51 and DC = 94. What is LM?

Accepted Answer

72.5

Question 17

$\overline{LM}$ is the midsegment of ABCD. AB = x + 8, LM = 4x + 3, and DC = 306. What is the value of x?

Accepted Answer

44

Question 18

Find m∠1 and m∠3 in the kite. The diagram is not to scale.

Accepted Answer

40, 50

Answer

40, 40

Answer

50, 40

Answer

50, 50

Question 19

m∠R = 140 and m∠S = 100. Find m∠T. The diagram is not to scale.

Accepted Answer

20

Question 20

Find the values of the variables and the lengths of the sides of this kite.

Accepted Answer

x = 1, y = 6; 4, 7

Answer

x = 1, y = 6; 1, 9

Answer

x = 6, y = 1; 1, 9

Answer

x = 6, y = 1; 4, 4

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