Question

If the measure of arc GH= 90° and the measure of arc EF= 45°, calculate m∠GDH.

Answer 1

∠ GDH = 67.5°

Explanation:

The measure of the chord- chord angle GDH is half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

∠ GDH =
`(1)/(2)`(GH + EF) =
`(1)/(2)` (90 + 45)° = 0.5 × 135° = 67.5°