Angle ABD measures (4x + 10)o. Angle ACD measures (5x − 2)o.
Circle E is shown. Angles A B D and A C D intercepts arc A D. Angles B A C and B D C intercepts arc B C.
What is the measure of arc AD?
12°
58°
96°
116°
Answers
Given : Angle ABD measures (4x + 10)°. Angle ACD measures (5x − 2)°.
To find : measure of arc AD
Solution:
∠ABD = ∠ACD ( angle by same chord AD )
∠ABD = (4x + 10)°
∠ACD = (5x - 2)°
=>(4x + 10)° = (5x - 2)°
=> x = 12
∠ABD = (4x + 10)° = ( 4 * 12 + 10)° = 58°
∠ACD = (5x - 2)° = ( 5 * 12 - 2)° = 58°
∠AOD = 2∠ABD = 2∠ACD ( angle by arc AD at center = 2 angle by same arc AC in other arc segment)
=> ∠AOD = 2 * 58°
=> ∠AOD = 116°
Measure of arc AD = 116°
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