Question

Given: m
KL
=25°, m
MJ
=85°
Find: m∠MEJ

Answer 1

30°

Explanation:

x=(a-b)/2 because of secants exterior angles

x=(85-25)/2 Substitution

x=60/2 Algebra

x=30° Answer

Answer 2

30°

Explanation:

If the measure of the arc KL is 25°, then the central angle KOL has measure 25° and the inscribed angle KML subtended on the arc KL has the measure 12.5°.

If the measure of the arc MJ is 85°, then the central angle MOJ has measure 85° and the inscribed angle MLJ subtended on the arc MJ has the measure 42.5°.

Thus, the measure of the angle ELM is 180°-42.5°=137.5°.

Consider triangle EML. In this triangle,

m∠MEL=180°-137.5°-12.5°=30°.

Thus, m∠MEJ=30°.