Find the measure of CBE

<CBE = 119°

Explanation:

Given:

m<EBF = 61°

Required:

m<CBE

SOLUTION:

Since <DBE is a right angle, <ABE is also a right angle, and is equal to 90°.

m<ABF + m<EBF = 90° (angle addition postulate)

m<ABF + 61° = 90° (Substitution)

m<ABF = 90 - 61 (subtracting 61 from both sides)

m<ABF = 29°

m<ABF = m<CBD (vertical angles are congruent)

m<CBD = 29°

m<DBE = 90° (right angle)

m<CBD + m<DBE = m<CBE (Angle Addition Postulate)

29° + 90° = m<CBE (substitution)

119° = m<CBE