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Chapter 3: Q26 (page 98)

Find the measures of ∠1and ∠2.

Short Answer

Expert verified

The measure of ∠1and∠2are 35°and125°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¯is parallel to TR¯and MT¯is a transversal. So, the interior angles on the same side of the transversal is supplementary.

m∠TMN+m∠MTR=18085+m∠MTR=180

m∠MTR=180−85=95

03

Step 3. Apply the definition of exterior angles.

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

m∠1+m∠S=30+m∠MTRm∠1+90=30+95m∠1=35

04

Step 4. Description of step.

Since TS¯parallel to NR¯and RS¯, the value is ∠R=90.

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

m∠NRT+∠1=90m∠NRT=90−35=55

05

Step 5. Description of step.

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

m∠2+55=180m∠2=180−55=125

Therefore, the measure of ∠1and∠2are 35°and125°respectively.

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