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Chapter 3: Q9. (page 112)

Find the measures of the numbered angles.

XYZis regular.

Short Answer

Expert verified

The measures of鈭�1,鈭�2 and鈭�3 is60掳,60掳 and120掳 respectively.

Step by step solution

01

Step 1. Description of step.

A regular triangle is a triangle in which all the three sides are congruent and all interior angles are congruent.

02

Step 2. Description of step.

For triangle XYZ, a measure of each angle is

=1803=60掳

Therefore, m鈭�XZY=m鈭�1=m鈭�2=60掳.

03

Step 2. Apply the exterior angle theorem.

The measure of an exterior angle is equal to the sum of measure of remote interior angles.

In 螖XYZ,鈭�1,鈭�2 are remote interior angles and鈭�3 is an exterior angle than by exterior angle theorem,

m鈭�3=m鈭�1+m鈭�2=60+60=120掳

Therefore, the measures of鈭�1,鈭�2 and鈭�3 is60掳,60掳 and120掳 respectively.

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Most popular questions from this chapter

Name several lines skew to

Exercises 23-29 refer to the diagram in step 2 of exercise 22.

Name four planes parallel toFL鈫�.

If m鈭�5=m鈭�6+20, find m鈭�1

Classify each pair of angles as alternate interior angles, same-side interior angles, or corresponding angles.

and

State the postulate or theorem that justifies each statement.

鈭�3鈮�鈭�6
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