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119Course 3 • Chapter 5 Triangles and the Pythagorean Theorem

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For Exercises 1 and 2, write and solve an equation to find each missing length. Round to the nearest tenth if necessary.

1. An observer is standing 20 feet

20 ft

25 ftx

from a tree with a hanging birdhouse. She is looking at the birdhouse. How far from the groundis the birdhouse? Round to the nearest tenth if necessary.

2. Kenneth wants to wrap a collapsible fishing

18 in.

x in.

10 in.

rod in the box shown at the right. Find the length of the diagonal of the box. Round to the nearest tenth if necessary.

For Exercises 3 and 4, find the distance between each pair of points with the given coordinates. Round to the nearest tenth if necessary.

3. (4.25, 5.5), (3.5, 0)

4. (-2, 4), (-5, -2)

Find the value of x in each figure.

5.

62°

x° (x°+14°)

6.

(2x + 1)°

(x + 35)°

7. A shelf is in the shape of a triangle. Find the angles of the triangle if the measures of the angles are in the ratio x : x : 4x.

Test, Form 3B

1.

2.

3.

4.

5.

6.

7.

x2 + 202 = 252; 15 ft

102 + 182 = x2; 20.6 in

5.6 units

6.7 units

24

48

30°, 30°, 120°

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120 Course 3 • Chapter 5 Triangles and the Pythagorean Theorem

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8. What is true about the angles in an equilateral triangle?

9. What is the perimeter of the triangle?

x in. 3 in.

4 in.

10. Find the measure of an exterior angle of a regular decagon.

11. Find the sum of the measures of the interior angles of a 50-gon.

12. The side view of a house (the “side elevation”) is often in the shape of a pentagon. If the angle at the roof is 150° and there are two other angles of 90°, what is the sum of the measures of the other two angles?

13. A triangle has side lengths of 10 inches, 24 inches, and 26 inches. Is the triangle a right triangle? Explain.

14. Use the proof to find the missing reason. Given: two parallel lines cut by a

transversal, m∠5 = 4x, and m∠7 = 96°

Prove: x = 24 Proof:

Statements Reasons 1. m∠5 = 4x, m∠7 = 96° Given 2. m∠5 = m∠7 ?3. 4x = 96 Substitution 4. x = 24 Division Property

Test, Form 3B (continued)

321

4

5678

8.

9.

10.

11.

12.

13.

14.

36˚

210˚

8,640˚

Corresponding angles have equal measures.

12 in.

Sample answer: They are all 60˚.

Yes; 102 + 242 = 262

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