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Chapter 3: Q26 (page 98)

Find the measures of 鈭�1and 鈭�2.

Short Answer

Expert verified

The measure of 鈭�1and鈭�2are 35掳补苍诲125掳respectively.

Step by step solution

01

Step 1. Observe the figure and highlight angle 1 and angle 2.

02

Step 2. Description of step.

Consider MN炉is parallel to TR炉and MT炉is a transversal. So, the interior angles on the same side of the transversal is supplementary.

m鈭�TMN+m鈭�MTR=18085+m鈭�MTR=180

m鈭�MTR=180鈭�85=95

03

Step 3. Apply the definition of exterior angles.

From the figure, it can be observed that 鈭�1and鈭�Sare remote interior angles. Therefore,

m鈭�1+m鈭�S=30+m鈭�MTRm鈭�1+90=30+95m鈭�1=35

04

Step 4. Description of step.

Since TS炉parallel to NR炉and RS炉, the value is 鈭�R=90.

If two lines are parallel and the line is perpendicular to one line then it is perpendicular to other line.

m鈭�NRT+鈭�1=90m鈭�NRT=90鈭�35=55

05

Step 5. Description of step.

Since the sum of the same side interior angles is supplementary.

m鈭�2+55=180m鈭�2=180鈭�55=125

Therefore, the measure of 鈭�1and鈭�2are 35掳and125掳respectively.

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Most popular questions from this chapter

Write proofs in two-column form.

Given: k鈭�l

Prove: 鈭�1is supplementary to 鈭�7

Name the two lines and the transversal that form each pair of angles.

and

Classify each pair of angles as alternate interior, same side interior

or corresponding angles

and

Name five lines parallel to plane ABCD

Find the values of xand y
See all solutions

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