Question

Given AFGH is a cyclic quadrilateral, find the value below:

Answer 1

238°

Explanation:

In a cyclic quadrilateral, the pair of opposite angles add up to 180 degrees.

So, the angle "21x - 2" and the angle "38x + 5" add up to 180.

So, we can write an equation and solve for x first:

`21x-2+38x+5=180\\59x+3=180\\59x=180-3\\59x=177\\x=3`

x = 3

Now, Arc FGH is DOUBLE of Angle A. Angle A is "38x + 5". We know x, so angle A is:

Angle A = 38x + 5 = 38(3) + 5 = 119

Thus, Arc FGH = 2 * 119 = 238°