Question

Given: GC bisects FGH. Determine the missing measure.a. m

Answer 1

Given that line segment, GC bisects ∠FGH

I made a sketch of the angles, they are not at scale.

That segment GC is an angle bisector indicates that it divides ∠FGH into halves. To determine the measure of the ∠FGC and ∠CGH you have to divide the measure of FGH by 2.

`\angle\text{FGC}=\angle\text{CGH}=\frac{\angle\text{FGH}}{2}`

a) ∠FGH=86º

`\begin{gathered} \angle\text{FGC}=(\angle FGH)/(2) \\ \angle\text{FGC}=(86º)/(2) \\ \angle\text{FGC}=43º \end{gathered}`

So, in this case, the measure of ∠FGC is 43º.

b) For this item you have to determine the measure of ∠FGH given that the measure of one of the angles determined by the bisector is ∠CGH. To determine the measure of ∠FGH you have to multiply ∠CGH by 2

`\begin{gathered} \angle\text{FGH}=2\cdot\angle\text{CGH} \\ \angle\text{FGH}=2\cdot28º \\ \angle\text{FGH}=56º \end{gathered}`