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Which of the following angles must have a measure of 95°

Which Of The Following Angles Must Have A Measure Of 95 class=

Sagot :

Since quadrilateral MNPQ is inscribed inside a circle, it means that it is a cyclic quadrilateral. For a cyclic quadrilateral, the opposite angles are supplementary. This means that their sum is 180 degrees.

This means that

M and P are opposite angles

angle M + angle P = 180 degrees

Also,

N and Q are opposite angles

angle N + angle Q = 180 degrees

We were told that segment MN is part of ray MR. This means that angle PNR is adjacent to angle PNM. The sum of the adjacent angles is 180 degrees

If angle PNR = 95 degrees, then,

angle PNM = 180 - 95 = 85 degrees

angle PNM is the same as angle N

We know that

angle N + angle Q = 180 degrees

85 + angle Q = 180

angle Q = 180 - 85

angle Q = 95 degrees

Thus, the correct option is

D) angle Q

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