Question

If the angles of a the figure, points P, Q, R and S lie on a circle. Find the values of x and y. are ​

Answer 1

Answer:

[tex]Answer:  The correct option is (A) 41°.

Step-by-step explanation:  Given that quadrilateral OPQR is inscribed in circle N as shown in the figure.

Also, ∠ROP = (x+17)°  and  ∠RQP = (6x-5)°.

We are to find the measure of ∠ROP.

Since quadrilateral OPQR is inscribed in a circle, so it is a cyclic quadrilateral.

We know that the sum of the measures of opposite angles of a cyclic quadrilateral is 180°.

So, in cyclic quadrilateral OPQR, we have

\begin{gathered}m\angle ROP+m\angle RQP=180^\circ\\\\\Rightarrow (x+17)^\circ+(6x-5)^\circ=180^\circ\\\\\Rightarrow (7x+12)^\circ=180^circ\\\\\Rightarrow 7x^\circ=168^\circ\\\\\Rightarrow x^\circ=\left(\dfrac{168}{7}\right)^\circ\\\\\Rightarrow x^\circ=24^\circ.\end{gathered}m∠ROP+m∠RQP=180∘⇒(x+17)∘+(6x−5)∘=180∘⇒(7x+12)∘=180circ⇒7x∘=168∘⇒x∘=(7168)∘⇒x∘=24∘.

Therefore, we get

m\angle ROP=(x+17)^\circ=(24+17)^\circ=41^\circ.m∠ROP=(x+17)∘=(24+17)∘=41∘.

Thus, the measure of angle ROP is 41°.

Option (A) is CORRECT.