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In the figure, PQR is a straight line. Find the values of x and y.


Question

In the figure, PQR is a straight line. Find the values of x and y.

Options

A) x = 22.5\(^{\circ}\), y = 33.75\(^{\circ}\)

B) x = 15\(^{\circ}\), y = 52.5\(^{\circ}\)

C) x = 22.5\(^{\circ}\), y = 45.0\(^{\circ}\)

D) x = 56.25\(^{\circ}\), y = 11.5\(^{\circ}\)

The correct answer is A.

Explanation:

\(\frac{2}{3}\) + 3y + 45\(^{\circ}\) = 180\(^{\circ}\)

3x + 6y + 90\(^{\circ}\) = 360\(^{\circ}\)

3x + 67 = 270.......(i) x 2, 5x + y + y = 180\(^{\circ}\)

5x + 2y = 180\(^{\circ}\).......(ii) x 6

6 x 12y = 540..........(iii)

30x + 12y = 1080.........(iv)

egn(iv) - eqn(iii)

24x = 540

x = 22.5 and y = 33.75\(^{\circ}\)


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