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,
[tex]m\angle RQS=7x+18\ \ \ and\\m\angle TQS=9x+2[/tex]
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.
[tex]\therefore \angle RQS+\angle SQT=180\°[/tex]
Now substituting the given values, we get;
[tex](7x+18)+(9x+2)=180\°\\\\7x+9x+20=180\°\\\\16x=180-20=160\°\\\\x=\frac{160}{16}=10\°[/tex]
We get the value of 'x'.
By substituting the value of x, we can find the measure of ∠RQS.
[tex]m\angle RQS=7x+18=7\times10+18=70+18=88\°[/tex]
[tex]m\angle TQS=9x+2=9\times10+2=90+2=92\°[/tex]
Hence the measure of ∠RQS is 88°.
