Question

Quadrilateral OPQR is inscribed inside a circle as shown below. What is the measure of angle P? You must show all work and calculations to receive credit.

An answer with work shown would be aprreciated :D

Answer 1

The measure of angle P is 43°

Explanation:

If a quadrilateral is inscribed inside a circle, the sum of opposite angles is always equals 180 degrees.

The angle POR is opposite to the angle PQR, and the angle OPQ is opposite to the angle ORQ.

So we have that:

mOPQ + mORQ = 180°

y + 3y + 8 = 180

4y = 172

y = 43°

So the measure of angle P is 43°

Answer 2

mes angle P = mes arc (ORQ) / 2

mes angle R = mes arc(OPQ) / 2

But mes arc(OPQ+ORQ) = 360° & ===> mes angle (P+R) =arc(OPQ+ORQ) /2

= 180°. Then P+R =180°.

Replace P & R by their respective values: y°+3y°+8°=180°
4y° = 172° ===> y°=43°