Asim is proving that the measure of ∠PQR is equal to two times the measure of ∠PQS. Which statement correctly completes Asim's proof?
Statement: "∠QRS is a straight angle because it is a supplementary angle to ∠PQS."
Explanation: By definition, a straight angle measures 180 degrees. Since ∠QRS is a supplementary angle to ∠PQS, they add up to form a straight angle. Therefore, the measure of ∠PQS is half of 180 degrees, which is 90 degrees. And since Asim is proving that the measure of ∠PQR is equal to two times the measure of ∠PQS, we get:
∠PQR = 2 × ∠PQS
∠PQR = 2 × 90
∠PQR = 180
Therefore, the measure of ∠PQR is indeed equal to twice the measure of ∠PQS.
To complete Asim's proof, the correct statement would be:
Statement: ∠PQR and ∠PQS are vertical angles.
Explanation: Vertical angles are formed by the intersection of two lines. They have equal measures, which means that if ∠PQR and ∠PQS are vertical angles, then their measures will be equal. Therefore, the measure of ∠PQR is equal to two times the measure of ∠PQS.