Question

Find the measure of the indicated arcs or central angles in OA. DG is a diameter.

Answer 1

Arc DE = 90°

m<GAB = 82°

Arc DC = 49°

Explanation:

Given:

m<EAF = 74°

m<EAD = right angle = 90°

Arc BG = 82°

Required:

Arc DE,

<GAB, and

Arc DC

Solution:

Recall that the central angle measure = the intercepted arc measure.

Therefore:

✔️Arc DE = m<EAD

Arc DE = 90° (Substitution)

✔️m<GAB = arc BG

m<GAB = 82° (Substitution)

✔️Arc DC = m<CAD

Find m<CAD

m<CAD = ½(180 - m<GAB)

m<CAD = ½(180 - 82)

m<CAD = 49°

Arc DC = m<CAD

Arc DC = 49°