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Chapter 12: Q13. (page 695)

Which angles have the same measure as 鈭�1 in the diagram?

Short Answer

Expert verified

The angles that have the same measure as 鈭�1 are 鈭�4,鈭�5,and鈭�8.

Step by step solution

01

Step 1. Given Information.

The provided figure is

02

Step 2. Concepts used.

Transversal and parallel lines

When two lines are crossed by another line, it is known as transversal. If two parallel lines are intersected by a transversal line then the corresponding angles are equal, alternate interior angles and alternate exterior angles are equal.

03

Step 3. Explanation.

Since vertically opposite angles are equal, m鈭�1=m鈭�4.

Since鈭�1 and 鈭�5 are a pair of corresponding angles,m鈭�1=m鈭�5.

Since 鈭�1 and 鈭�8 are a pair of corresponding angles, m鈭�1=m鈭�8.

04

Step 4. Conclusion.

The angles that have the same measure as 鈭�1 are 鈭�4,鈭�5,and鈭�8.

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Most popular questions from this chapter

Tell whether the angles are corresponding, alternate, interior, or alternate exterior angles.

鈭�2and鈭�7

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

m鈭�1=140掳m鈭�2=40掳

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.

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

m鈭�5=98掳m鈭�6=72掳

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.
See all solutions

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