What is the measure of arc AD?

Angle ABD measures (4x + 10). Angle ACD measures

(5x - 2)

GO

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°