Question

A teacher draws Circle O, angle RPG and angle ROQ as shown. The teacher asks the students to select the correct claim about the relationship between the measure of angle RPQ and the measure of angle ROQ. Claim 1: The measure of angle RPQ is equal to the measure of angle ROQ. Claim 2: The measure of angle ROQ is twice the size of the measure of angle RPQ. Which claim is correct? Justify your answer.

Answer 1

Answer

Claim 2 is the correct answer.

Claim 2: The measure of angle ROQ is twice the size of the measure of angle RPQ.  is the correct answer.

Solution

The circle centre can be written as O.

RQ be the arc. ∠ROQ  be the angle of arc RQ

and ∠RPQ may be the angle of other side of arc RQ

So  The measure of angle ROQ is twice the size of the measure of angle RPQ.