Question

The measure of ⏜ is 161°, and the measure of ⏜ is 107°.

What is the measure of ∠ ?

Answer 1

m<AEB = 46°

Explanation:

Given:

Arc AD = 161°

Arc BC = 107°

Required:

m<AEB

Solution:

Vertex angle = ½(sum of intercepted arcs) => Theorem for angle inside a circle and its intercepted arcs)

This:

m<AED = ½(AD + BC)

m<AED = ½(161 + 107) => Substitution

m<AED = ½(268) = 134°

✔️m<AEB = 180° - m<AED => Linear pair theorem

m<AEB = 180° - 134° => substitution

m<AEB = 46°