Given:
EH is a diameter of the circle.
Measure of arc EF = (10x + 8)°
Measure of arc GH = (11x)°
m∠FDG = 67°
To find:
The value of x, the measure of arc EF and the measure of arc GH in degrees.
Solution:
The measure intercepted angle is equal to the measure of the central angle.
m∠EDF = m(ar EF)
m∠EDF = (10x + 8)°
m∠GDH = m(ar GH)
m∠GDH = (11x)°
Sum of the adjacent angles in a straight line is 180°.
m∠EDF + m∠FDG + m∠GDH = 180°
10x° + 8° + 67° + 11x° = 180°
21x° + 75° = 180°
Subtract 75° from both sides.
21x° = 105°
Divide by 21 on both sides.
x° = 5°
The value of x is 5.
Measure of arc EF = (10(5) + 8)°
= 58°
The measure of arc EF is 58°.
Measure of arc GH = (11(5))°
= 55°
The measure of arc GH is 55°.