Question

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

A) 68 degrees
B) 34 degrees
C) 56 degrees
D) 112 degrees
E) None of the above.

Answer 1

The measure of ∆BGF in the diagram given that CD bisects ∆AGF and m∆AGD = 68° is 136°, which is not an option listed in the question. Thus, there seems to be a discrepancy in the information provided.

Step-by-step explanation:

The student is asked to find the measure of ∆BGF given that CD bisects ∆AGF and m∆AGD = 68°. Since CD bisects ∆AGF, this means that ∆AGD and ∆DGF are congruent and therefore have the same measure. As m∆AGD is given as 68°, the measure of ∆DGF is also 68°.

Now, ∆BGF is composed of two angles: ∆AGD and ∆DGF. We add the measures of these two angles to find the measure of ∆BGF. So, m∆BGF = 68° + 68° = 136°. However, this option is not listed in the multiple-choice answers, which means that there is an error in either the query or the possible answers provided.