Question

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?

Answer 1

Answer:

The measure of angle PQR is 74 degrees

Step-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