Question

Find the measure of the missing angles.

Answer 1

d = 105° , e = 32° , f = 43°

Explanation:

d and 105° are vertically opposite angles and are congruent , then

d = 105°

e and 32° are vertically opposite angles and are congruent , then

e = 32°

105° , e and f lie on a straight line and sum to 180° , that is

105° + e + f = 180°

105° + 32° + f = 180°

137° + f = 180° ( subtract 137° from both sides )

f = 43°

Answer 2

d= 105° f= 43° e= 32°

Explanation:

angle d = 105° ( vertically opposite angles are equal)

f°+d°+32°= 180 (angles on a straight line)

f+105+32= 180

f+137=180

f= 180-137= 43°

f= 43°

angle .d+f+e = 180° (angles on a straight line)

105+43+e = 180°

148+ e = 180°

e = 180-148

e = 32°

therefore,

d= 105° f= 43° e= 32°