Find the measure of .
A) 69°
B) 66°
C) 19°
D) 208°
E) 61°

Question

Find the measure of  . 
A) 69° 
B) 66° 
C) 19° 
D) 208° 
E) 61°

Quizplus · Accepted Answer

The measure of an angle in a circle intercepted by the same arc is equal. Therefore, the measure of angle 11eb69da_9ee6_e138_af94_3da3464112be_TB8311_11 is equal to the measure of angle 11eb69da_9ee6_e139_af94_7d6f931cae7d_TB8311_11. We can set both angles equal to x. Then, using the fact that angles around a point sum to 360°, we can set up the equation:

x + x + 66° + 45° = 360°

Simplifying, we get:

2x + 111° = 360°

Subtracting 111° from both sides:

2x = 249°

Dividing by 2:

x = 124.5°

Therefore, the measure of both angles is 124.5°, which is closest to choice B (66°).

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