Question

GEOMETRY 100POINTS!!!!!​

Answer 1

C) 68

Explanation:

Answer 2

C) 68°

Explanation:

An arc measure is equal to its corresponding central angle measure.

Angles around a point sum to 360°.

Therefore, the sum of arcs GC, CD, DE, EF and FG is 360°.

To find the measure of arc FG, set the sum of all the minor arcs to 360° and solve for x:

`\begin{aligned}\overset{\frown}{GC}+\overset{\frown}{CD}+\overset{\frown}{DE}+\overset{\frown}{EF}+\overset{\frown}{FG}&=360^(\circ)\\85^(\circ)+75^(\circ)+(-9x-2)+(x+76)+(x+70)&=360^(\circ)\\85+75-9x-2+x+76+x+70&=360\\304-7x&=360\\-7x&=56\\x&=-8\end{aligned}`

Substitute the found value of x into the expression for arc FG:

`\begin{aligned}\overset{\frown}{FG}&=x+76\\&=-8+76\\&=68^(\circ)\end{aligned}`

Therefore, the measure of arc FG is 68°.