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Chapter 3: Q10. (page 112)

Find the measures of the numbered angles.

Short Answer

Expert verified

The measures of鈭�1,鈭�2,鈭�3,鈭�4,鈭�5 and鈭�6 is58掳,90掳,32掳,87掳,35掳 and55掳 respectively.

Step by step solution

01

Step 1. Label the given diagram. 

02

Step 2. Description of step.

Consider 螖BEC, by an angle sum theorem,

m鈭�1+32+90=180m鈭�1=180鈭�122=58掳

03

Step 3. Description of step.

ABis parallelCDthen鈭�5 and鈭�ACDare alternate interior angles then

m鈭�5=m鈭�ACD=35掳.

ADis parallelBCthen鈭�3 and鈭�ACB are alternate interior angles then

m鈭�3=m鈭�ACB=32掳.

04

Step 4. Description of step.

From the given figure, it can be observed thatm鈭�2=90掳

05

Step 5. Description of step.

Consider 螖ADC, by an angle sum theorem,

m鈭�3+m鈭�4+35=18058+m鈭�4+35=180m鈭�4=180鈭�93=87掳

06

Step 6. Description of step.

Consider 螖AEB, by an angle sum theorem,

m鈭�2+m鈭�5+m鈭�6=18090+35+m鈭�6=180m鈭�6=180鈭�125=55掳

Therefore, the measures of鈭�1,鈭�2,鈭�3,鈭�4,鈭�5 and鈭�5is58掳,90掳,32掳,87掳,35掳 and55掳respectively.

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Most popular questions from this chapter

State the postulate or theorem that justifies each statement.

鈭�3 is supplementary to鈭�5

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

and

The blue line is a transversal.

a. Name four pairs of corresponding angles.

b. Name two pairs of alternate interior angles.

c. Name two pairs of same-side interior angles.

d. Name two pairs of angles that could be called alternate exterior angles.

e.

Complete each statement with the word always, sometimes, or never.

Two planes parallel to the same plane are ?parallel to each other.

Write proof in two column form

Given: k鈭�l

Prove: 鈭�2鈮�鈭�7
See all solutions

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