If B is in the interior of ∠DEF, m∠DEB = 27.2, and m∠DEF = 92.5, find m∠BEF. (Lesson 2-7)

m∠BEF = 65.3°

Step-by-step explanation:

Given:

m∠DEB = 27.2,

m∠DEF = 92.5

Required:

m∠BEF

SOLUTION:

Since B is the interior of ∠DEF, it means ∠DEB and ∠BEF are adjacent angles that make up ∠DEF. And they share the same side, BE.

Therefore:

m∠BEF + m∠DEB = m∠DEF (angle addition postulate)

m∠BEF + 27.2 = 92.5

Subtract 27.2 from each side

m∠BEF + 27.2 - 27.2 = 92.5 - 27.2

m∠BEF = 92.5 - 27.2

m∠BEF = 65.3°