Question

In the accompanying

diagram of AABC, AC is extended
to D, DEF, BEC, AFB, MLB = 50, m_BEF = 25, and
mLACB = 65. What is mLD?
50° B
F
25°
E
65°
А
С
D
040
0 45
O 50
o 55

Answer 1

A. 40°

Explanation:

Given:

m<BEF =25°

m<B = 50°

m<ACB = 65°

Required:

m<D

SOLUTION:

m<CED = m<BEF (vertical angles theorem)

m<CED = 25° (Substitution)

m<ACB + m<DCE = 180° (linear pair theorem)

65° + m<DCE = 180° (substitution)

Subtract 65 from both sides

m<DCE = 180° - 65°

m<DCE = 115°

m<DCE + m<CED + m<D = 180° (sum of triangle)

115° + 25° + m<D = 180° (substitution)

140° + m<D = 180°

Subtract 140° from both sides

m<D = 180° - 140°

m<D = 40°