Answer:
116°
Step-by-step explanation:
Given that :
∠ ABD measures (4x + 10)
∠ ACD measures (5x - 2)
Then
∠ABD = ∠ACD ( rule : angle by same chord AD )
∠ABD = (4x + 10)°
∠ACD = (5x - 2)°
so we can as well say that :
(4x + 10)° = (5x - 2)°
4x - x = -10 -2
- x = - 12
x = 12
∠ABD = (4x + 10)°
= ( 4 × 12 + 10)°
= 58°
∠ACD = (5x - 2)°
= ( 5 * 12 - 2)°
= 58°
∠AOD = 2∠ABD = 2∠ACD ( since angle by arc AD at center is twice the angle by same arc AC in other arc segment)
∠AOD = 2 × 58°
∠AOD = 116°
Measure of arc AD = 116°
