Question

Circle R has a radius of line segment of QR and QP is a tangent to circle R at point Q.

(Picture attached)

(a) What is the measure of RQP? Explain your answer.

(b) What is the value of x? Explain your answer with work.

(c) What is the measure of QRP? Explain your answer with work.

(d) What is the measure of RPQ? Explain your answer with work.

Answer 1

QUESTION 1 a

We were given that, line PQ is a tangent to the circle.


This tangent will meet the radius or diameter at an angle of

`90 \degree`


This implies that,

`< \: RQP = 90 \degree`


Question 1b


The other two angles of right triangle PQR are complementary.

This implies that,




`(5x + 20) + 3x = 90 \degree`


We group like terms to get,



`5x + 3x = 90 - 20`


This implies that,



`8x = 70`



`x = (70)/(8)`



`x = 8.75`


Question 1c

We substitute the value of x to determine the


value angle QRP.



`\: < \: QRP = 5(8.75) + 20 = 63.75 \degree`

Question 1d

We substitute the value of x to determine the value angle RPQ.



`\: < RPQ \: = 3(8.75) = 26.25 \degree`