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°.
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°.
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