Question

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

Answer 1

Answer:

A.88°

Step-by-step 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;

$(7x+18)+(9x+2)=180\°\\\\7x+9x+20=180\°\\\\16x=180-20=160\°\\\\x=\frac{160}{16}=10\°$

We get the value of 'x'.

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

$m\angle RQS=7x+18=7\times10+18=70+18=88\°$

$m\angle TQS=9x+2=9\times10+2=90+2=92\°$

Hence the measure of ∠RQS is 88°.