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Chapter 12: Q5. (page 689)

Tell whether the angles are complementary, supplementary, or neither.

m鈭�5=58掳m鈭�6=32掳

Short Answer

Expert verified

The pair of angles are complementary to each other.

Step by step solution

01

Step 1. Given Information.

The choices are: complementary, supplementary, or neither.

02

Step 2. Concept used.

If the sum of two angles is 90掳 then the angles are called complementary angles and if the sum is 180掳 then the angles are called supplementary angles.

03

Step 3. Calculation.

Calculate the sum of the measures of the two angles.

m鈭�5+m鈭�6=58掳+32掳=90掳

04

Step 4. Conclusion.

Since the sum of angles is 90掳, the given two angles are a complementary angle pair.

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Most popular questions from this chapter

A transversal intersects lines mand n. If the corresponding angles are congruent, what can you conclude about lines m and n?

The diagram shows the sculpture Clothespin casting a shadow. In the diagram, 鈭�2is the angle of the sun above the horizon.

  1. At a certain time of the day, m鈭�1=148掳, and the shadow has a length of 72 feet. Use a calculator to find the height of the sculpture. Round to the nearest tenth.
  2. At a certain time of the day, m鈭�1=135掳. How is the length of the shadow related to the height of the sculpture? Explain your reasoning.

Challenge: Use the diagram.

  1. Write expressions for m鈭�1,m鈭�2,andm鈭�3 in terms of x and y. Explain your reasoning.
  2. Use the expressions you wrote in part (a) to show that the sum of the measures of the angles in 螖ABC is 180掳.

In Exercises 29 and 30, tell whether a triangle exists for the given description. If so, classify the triangle by its angles. If not, explain why not.

Two of the angles are complementary.

In the diagram shown, m鈭�1=35掳and m鈭�3=110掳. What is m鈭�5?

  1. Tell how 鈭�1and 鈭�2 arerelated. Then find m鈭�2.
  2. Tell how 鈭�3and 鈭�4 arerelated. Then find m鈭�4.
  3. Use what you know about the sum of the measures of the angles of a triangle to find m鈭�5.
See all solutions

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