Question

Can someone please solve this

Answer 1

Answer:

RPQ = 239°

Step-by-step explanation:

Since SP is a straight line going through the center of a circle, it is a diameter.

We can say that m<SOR and m<ROP are supplementary and add up to 180° because they form a straight line. We can set up an equation:

m<SOR + m<ROP = 180°

We can substitute in the value of m<SOR:

31° + m<ROP = 180°

m<ROP = 149°

Next, we can also say that m<SOQ and m<QOP are supplementary because they form a straight line. Also, since QO is perpendicular to SP, we can say that both m<SOQ and m<QOP equal to 90°.

Now, we can say that m<ROQ (reflex angle) is equal to the sum of m<QOP and m<ROP from angle addition postulate. We can write the equation:

m<ROQ = m<QOP + m<ROP

m<ROQ = 90° + 149° = 239°

The reflex angle <ROQ cuts the arc RPQ, so they would have the same measure. So, arc RPQ = 239°