Question

If RT is a diameter of Q, Find m A.88°
B.89°
C.92°
D.101°

Answer 1

A.88°

Explanation:

Given,

RT is the diameter of the circle with center Q.

We have to find the measure of ∠RQS.

Solution,

`m\angle RQS=7x+18\ \ \ and\\m\angle TQS=9x+2`

Since RT is the diameter. That is it makes a straight angle at the center Q.

And measure of straight angle is 180°.

So we can say that ∠RQS and ∠SQT makes a straight angle.

`\therefore \angle RQS+\angle SQT=180\°`

Now substituting the given values, we get;

`(7x+18)+(9x+2)=180\°\\\\7x+9x+20=180\°\\\\16x=180-20=160\°\\\\x=(160)/(16)=10\°`

We get the value of 'x'.

By substituting the value of x, we can find the measure of ∠RQS.

`m\angle RQS=7x+18=7*10+18=70+18=88\°`

`m\angle TQS=9x+2=9*10+2=90+2=92\°`

Hence the measure of ∠RQS is 88°.