Question

find the measure of the arc indicated

Answer 1

Answer:

Step-by-step explanation:

Angle GPE is an inscribed angle.  It intercepts arc GFE.  The rule for inscribed angles and the arcs they intercept is that the angle is half the measure of the arc it intercepts.  Angle P is 96, so that means that arc GFE is twice that.  2(96) = 192.  We have arc FG as 92, so that means that arc FE is 192 - 92 which is 100 degrees.  The third choice down.

Answer 2

The measure of the unknown indicated arc is arcFE = 100degrees

Circle geometry

The sum of the opposite side of a quadrilateral is 180 degrees.

From the given diagram

The measure of arcGFE is twice the vertex angle <P
arcGFE = 2<P
arcGFE = 2(96)

arcGFE = 192 degrees

Determine the measure of arcFE

arcFE = arcGFE - arcFG
arcFE = 192 - 92
arcFE = 100degrees

Hence the measure of the unknown indicated arc is arcFE = 100degrees

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