Question 1:

Find the measure of A.

A

BC

145°44°

Question 1: SOLUTIONThe measure of an exterior angle is

the sum of the two remote interior angles.

44 145m A 101m A

A

BC

145°44°

101

Question 2:

Find DC if HL = 68.

HD

S

C

L

Question 2: SOLUTION

By the Midline Theorem, DC is half the length of HL.

HD

S

C

L

DC = 34

1 168 34

2 2HL

Question 3:

Find the sum of the exterior angles in a regular

dodecagon.

Question 3 SOLUTION:

The sum of the exterior angles in any polygon is always 360°.

360°

Question 4:Find the sum of the angles in a 62-gon.

Question 4 SOLUTION:Find the sum of the angles in a 62-gon.

int 2 180

62 2 180 60 180

10800

S n

10800°

Question 5:

Find the number of diagonals that can be

drawn in a regular octagon.

Question 5 SOLUTION:Find the number of diagonals that

can be drawn in a regular octagon.

3 8 8 3

2 28 5 40

202 2

n nd

20

Question 6:

How many sides does a pentadecagon

have?

Question 6 SOLUTION:

A pentadecagon has 15 sides.

15

Question 7:

Find the number of sides in a regular polygon whose exterior

angles each measure 7.5°.

Question 7 SOLUTION:

Find the number of sides in a regular polygon whose exterior angles each measure 7.5°.

360E

n

3607.5

n 7.5 360n

36048

7.5n

48

Question 8:Solve x2 + 5x = 84 by factoring.

What is the greater of the two solutions?

Question 8 SOLUTION:Solve x2 + 5x = 84 by factoring.

What is the greater of the two solutions?

x2 + 5x – 84 = 0

(x - 7)(x + 12) = 0

x - 7 = 0 x = 7

x + 12 = 0 x = -12

7

Question 9:

The sum of the interior angles of a polygon is 7740°. How many sides does the polygon have?

Question 9 SOLUTION:

The sum of the interior angles of a polygon is 7740°. How many sides does the polygon

have?

int 2 180

7740 2 180

43 2

45

S n

n

n

n

45

Question 10:

Find the measure of an interior angle in a regular

decagon.

Question 10 SOLUTION:Find the measure of an interior

angle in a regular decagon.

2 180 10 2 180

108 180 1440

14410 10

nI

n

144

Question 11:

A polygon has 54 diagonals. How many sides does the

polygon have?

Question 11 SOLUTION:A polygon has 54 diagonals. How

many sides does the polygon have?

3

2

n nd

354

2

n n

2 3 108 0n n

12 9 0n n

12 0 12

9 0 9

n n

n n

12

Question 12:

What is the measure of an exterior angle in a regular 72-gon?

Question 12 SOLUTION:

What is the measure of an exterior angle in a regular 72-gon?

5

360E

n 360

572

E

Question 13:

The measure of an angle in a regular polygon is 140°. How many sides does the polygon have?

Question 13 SOLUTION:The measure of an angle in a regular polygon is

140°. How many sides does the polygon have?

9

2 180nI

n

2 180140

n

n

140 2 180n n

140 180 360n n 40 360n

9n

Question 14:Find the measure of the

missing angle in the triangle.

36°

Question 14 SOLUTION:Find the measure of the missing angle in the triangle.

36°

54

180 – 90 – 36 = 54°

Question 15:The ratio of an interior angle

to an exterior angle in a regular polygon is 7:1.

How many sides does the polygon have?

Question 15 SOLUTION:The ratio of an interior angle to an exterior angle in a

regular polygon is 7:1. How many sides does the polygon have?

16

Interior and exterior angles are supplementary.

1x + 7x = 180

8x = 180

x = 22.5

Exterior angle = 22.5°

360 360 22.5

22.5 360

16

En nn

n

Question 16:

Find the measure of S.

HD

S

C

L

67°

82°

Question 16 SOLUTION:

Find the measure of S.

31

HD

S

C

L

67°

82°

67°

82°

180 – 82 – 67 = 31°

Question 17:Solve for x.

(x + 2)°

(2x - 18)°

(4x-11)° (2x + 8)°

(3x + 7)°

Question 17 SOLUTION:Solve for x.

(x + 2)°

(2x - 18)°

(4x-11)° (2x + 8)°

(3x + 7)°

46

int 2 180 5 2 180 540S n

(x+2)+(2x-18)+(4x-11)+(2x+8)+(3x+7)=54012x – 12 = 54012x = 552x = 46

Question 18:Find the number of diagonals

in a 16-gon.

Question 18 SOLUTION:Find the number of diagonals in a 16-gon.

104

3 16 16 3

2 216 13 208

1042 2

n nd

Question 19:

Solve x2 – 13x + 42 = 0 by factoring.

Then find the smaller of the two solutions.

Question 19 SOLUTION:Solve x2 – 13x + 42 = 0 by factoring.

Then find the smaller of the two solutions.

6

x2 – 13x + 42 = 0

(x – 7)(x – 6) = 0

x – 7 = 0 x = 7

x – 6 = 0 x = 6

Question 20:

Find the measure of an angle in a regular 18-gon.

Question 20 SOLUTION:Find the measure of an angle in a regular 18-gon.

160

2 180 18 2 180

1816 180 2880

16018 18

nI

n

Question 21:

The vertex angle in an isosceles triangle measures

62°. Find the measure of one base angle.

Question 21 SOLUTION:The vertex angle in an isosceles triangle measures 62°.

Find the measure of one base angle.

59

62°

x° x°

x + x + 62 = 180

2x + 62 = 180

2x = 118

x = 59

Question 22:The measure of an exterior

angle of a regular polygon is 15°. Find the number of

sides in the polygon.

Question 22 SOLUTION:The measure of an exterior angle of a regular polygon

is 15°. Find the number of sides in the polygon.

24

360E

n 360

15n

15 360n

24n

Question 23:How many sides does a

polygon have if it has 275 diagonals?

Question 23 SOLUTION:How many sides does a

polygon have if it has 275 diagonals?

25

3

2

n nd

3275

2

n n

550 3n n 2 3 550 0n n

25 22 0n n

25 0 25

22 0 22

n n

n n

The End!The End!