Question

In the diagram below, lines AB, CD, and EF all intersect at the common point E. If CD bisects angle AGF and angle AGD=68° then what is the measure of angle BGF ? Explain how you arrived at your answer.​

Answer 1

m<BGF = 44°

Explanation:

Since line CD bisects angle AGF, it implies that the measure of angle AGF is twice the measure of angle AGD.

m<AGD = 68°, therefore,

m<AGF = 2*AGD

m<AGF = 2*68°

m<AGF = 136°

m<AGF + m<BGF = 180° (linear pair)

136° + m<BGF = 180° (Substitution)

Subtract 136° from each side

m<BGF = 180° - 136°

m<BGF = 44°