Chapter Review 307

Chapter Review7Review Key Vocabulary

adjacent angles, p. 272vertical angles, p. 272congruent angles, p. 272complementary angles,

p. 278

supplementary angles, p. 278

congruent sides, p. 284kite, p. 294scale drawing, p. 300

scale model, p. 300scale, p. 300 scale factor, p. 301

Review Examples and Exercises

Vocabulary Help

7.27.2 Complementary and Supplementary Angles (pp. 276–281)

Tell whether the angles are complementary or supplementary. Then fi nd the value of x.

The two angles make up a right angle. So, the angles are complementary angles, and the sum of their measures is 90°.

(2x − 8) + 42 = 90 Write equation.

2x + 34 = 90 Combine like terms.

2x = 56 Subtract 34 from each side.

x = 28 Divide each side by 2.

So, the value of x is 28.

7.17.1 Adjacent and Vertical Angles (pp. 270–275)

Tell whether the angles are adjacent or vertical. Then fi nd the value of x.

The angles are vertical angles. Because vertical angles are congruent, the angles have the same measure.

So, the value of x is 123.

Tell whether the angles are adjacent or vertical. Then fi nd the value of x.

1.

x69

2.

(x 3) 84

123x

42

(2x 8)

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308 Chapter 7 Constructions and Scale Drawings

Tell whether the angles are complementary or supplementary. Then fi nd the value of x.

3.

(6x 1) 29

4.

(4x 10)x

7.37.3 Triangles (pp. 282–289)

Draw a triangle with a 3.5-centimeter side and a 4-centimeter side that meet at a 25° angle. Then classify the triangle.

Step 1: Use a protractor to draw a 25° angle.

9090

8010070

11060120

50130

4014

0

3015

0

20 160

10 170

0 180

10080

11070 12060 13050 14040 15030

1602017010

180025

Step 2: Use a ruler to mark 3.5 centimeters on one ray and 4 centimeters on the other ray.

Step 3: Draw the third side to form the triangle.

253.5 cm

4 cm

The triangle is an obtuse scalene triangle.

Draw a triangle with the given description.

5. a triangle with angle measures of 40°, 50°, and 90°

6. a triangle with a 3-inch side and a 4-inch side that meet at a 30° angle

Find the value of x. Then classify the triangle.

7.

x

49 8.

(x 12)

35

110

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Chapter Review 309

7.47.4 Quadrilaterals (pp. 292–297)

Draw a parallelogram with a 50° angle and a 130° angle.

Step 1: Draw a line.

Step 2: Draw a 50° angle and a 130° angle that each have one side on the line.

Step 3: Draw the remaining side. Make sure that both pairs of opposite sides are parallel and congruent.

Find the value of x.

9.

128

x 10.

95

80 x

38

11. Draw a rhombus with 5-centimeter sides and two 120° angles.

Use a centimeter ruler to measure the segment shown. Find the scale of the drawing.

12. 30 in. 13. 7.5 in.

7.57.5 Scale Drawings (pp. 298–305)

9090

8010070

11060120

50130

4014

0

3015

0

20 160

10 170

0 180

10080

11070 12060 13050 14040

9090

8010070

11060120

50130

4014

0

3015

0

20 160

10 170

0 180

10080

11070 12060 13050 14040 15030

1602017010

180050 130

50 130

A lighthouse is 160 feet tall. A scale model of the lighthouse has a scale of 1 in. : 8 ft. How tall is the model of the lighthouse?

1 in. —

8 ft =

x in. —

160 ft

1 in. —

8 ft ⋅ 160 ft = x in.

— 160 ft

⋅ 160 ft Multiplication Property of Equality

20 = x Simplify.

So, the model of the lighthouse is 20 inches tall.

model height

actual height

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