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Chapter 3: Q10. (page 112)

Find the measures of the numbered angles.

Short Answer

Expert verified

The measures of∠1,∠2,∠3,∠4,∠5 and∠6 is58°,90°,32°,87°,35° and55° respectively.

Step by step solution

01

Step 1. Label the given diagram. 

02

Step 2. Description of step.

Consider ΔBEC, by an angle sum theorem,

m∠1+32+90=180m∠1=180−122=58°

03

Step 3. Description of step.

ABis parallelCDthen∠5 and∠ACDare alternate interior angles then

m∠5=m∠ACD=35°.

ADis parallelBCthen∠3 and∠ACB are alternate interior angles then

m∠3=m∠ACB=32°.

04

Step 4. Description of step.

From the given figure, it can be observed thatm∠2=90°

05

Step 5. Description of step.

Consider ΔADC, by an angle sum theorem,

m∠3+m∠4+35=18058+m∠4+35=180m∠4=180−93=87°

06

Step 6. Description of step.

Consider ΔAEB, by an angle sum theorem,

m∠2+m∠5+m∠6=18090+35+m∠6=180m∠6=180−125=55°

Therefore, the measures of∠1,∠2,∠3,∠4,∠5 and∠5is58°,90°,32°,87°,35° and55°respectively.

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