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Chapter 5: Q10 (page 192)

One angle of an isosceles trapezoid has measured 57. Find the measures of the other angles.

Short Answer

Expert verified

The measure of other angles is 57,123and 123.

Step by step solution

01

Step 1. Draw and label the diagram.

The figure shows, isosceles trapezoid. Let the measure of angle B be 57.

02

Step 2. Apply the property of isosceles trapezoid.

The base angles of an isosceles trapezoid are congruent.

Consider an isosceles trapezoid ABCD such that,

鈭�A鈮�鈭�D;鈭�B鈮�鈭�C

Thereforem鈭�B=m鈭�C=57

03

Step 3. Description of step.

The sum of the same side interior angles is 180. Therefore,

m鈭�A+m鈭�B=180m鈭�A+57=180m鈭�A=180鈭�57=123

04

Step 4. Description of step.

Substitute 123 for m鈭�Ainto m鈭�A=m鈭�Dto find the value of m鈭�D.

m鈭�D=123

Therefore, the measure of other angles is 57,123and 123.

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