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in the circle below, find the measure of ∠CPE if the measure of arc BE = 100°, the measure of arc BD = 34°, and the measure of arc DC = 96°. The figure is not drawn to scale.

in the circle below find the measure of CPE if the measure of arc BE 100 the measure of arc BD 34 and the measure of arc DC 96 The figure is not drawn to scale class=

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reinhard10158

The central angle of a circle is twice any inscribed angle subtended by the same arc.

the angle DPB = the angle CPE

due to the rules of crossing lines.

and either of them is then

(arc angle BD + arc angle CE)/2

we know, that all arc angles in a circle together must be 360°, of course.

so, arc angle CE = 360 - BE - BD - DC =

= 360 - 100 - 34 - 96 = 130°

therefore, we have

CPE = (34 + 130)/2 = 164/2 = 82°

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