MATH SOLVE

4 months ago

Q:
# julio bisects angle PQR and labels a point on the bisector as S. He measures angle PQS with a protractor. The measure of angle PQS is 37 degrees. What is the measure of angle PQR?

Accepted Solution

A:

Answer:The measure of angle PQR is 74 degreesStep-by-step explanation:* Lets explain how to solve the problem- Bisect an angle means divide the angle into two equal parts in measures- Ex: If angle ABC is bisected by a ray BD then:- Angle ABC is divided into two equal parts in measure m∠ABD = m∠CBD and m∠ABC = m∠ABD + m∠CBD- So we can say measure of angle ABC is twice measure of angle ABD or twice measure of angle CBD* Lets solve the problem- Julio bisects angle PQR and labels a point on the bisector as S∴ m∠PQS = m∠RQS∴ m∠PQR = m∠PQS + m∠RQS∴ m∠PQR = 2 m∠PQS ⇒ (or 2 m∠RQS)- He measures angle PQS with a protractor and find its measure is 37 degrees∵ m∠PQS = 37°∴ m∠PQR = 2 × m∠PQS∴ m∠PQR = 2 × 37 = 74°∴ The measure of angle PQR is 74 degrees