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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$$^{\circ}$$

Discussion (4)

• Also in the third line, it should be 6y and not 67

• I mean 3x/2

• In the first line of the solution, I think it should be 3/2x and not 2/3

• $$\frac{2}{3}$$ + 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$$^{\circ}$$