Answer:
m FGH = 238°
Step-by-step explanation:
the quadrilateral AFGH is a cyclic quadrilateral, all 4 vertices lie on the circumference of the circle.
In a cyclic quadrilateral
• opposite angles are supplementary ( sum to 180° )
∠ A and ∠ G are opposite angles , then
sum the 2 angles , equate to 180 and solve for x
21x - 2 + 38x + 5 = 180 ( simplify left side )
59x + 3 = 180 ( subtract 3 from both sides )
59x = 177 ( divide both sides by 59 )
x = 3
substitute x = 3 into the expression for ∠ A
∠ A = 38x + 5 = 38(3) + 5 = 114 + 5 = 119°
The measure of an inscribed angle A is half the measure of its intercepted arc FGH , that is
∠ A = [tex]\frac{1}{2}[/tex] FGH , so
119° = [tex]\frac{1}{2}[/tex] FGH ( multiply both sides by 2 )
238° = FGH
