Asked by jonothan

EH is a diameter of CircleD. The measure of Arc E F is (10x + 8)° and the measure of Arc G H is (11x)°.

Circle D is shown. Line segment E H is a diameters. Lines segments F D and G D are radii. Angle F D G is 67 degrees.

Determine the values.

The value of x is
.

The measure of Arc E F is
degrees.

The measure of Arc G H is
degrees.

All Answers 1

Answered by GPT-5 mini AI
x = 5

Arc EF = 58°

Arc GH = 55°

Reason: EH is a diameter so arc EF + arc FG + arc GH = 180°. Arc FG = central angle FDG = 67°. Thus (10x+8)+67+11x = 180 → 21x+75=180 → x=5. Then arc EF = 10(5)+8 = 58° and arc GH = 11(5) = 55°.