Question

In ANOP, NP is extended through point P to point Q, m_OPQ = (9x – 19)°,

Answer 1

Answer:

The values of x and y are x = 6 and y = 9Step-by-step explanation:

MNOP is a parallelogram its diagonal MO and PN intersected at point A

In any parallelogram diagonals:

Bisect each other

Meet each other at their mid-point

In parallelogram MNOP

∵ MO and NP are its diagonal

∵ MO intersect NP at point A

- Point A is the mid-point pf them

∴ MO and NP bisect each other

∴ MA = AO

∴ PA = AN

∵ MA = x + 5

∵ AO = y + 2

- Equate them

∴ x + 5 = y + 2 ⇒ (1)

∵ PA = 3x

∵ AN = 2y

- Equate them

∴ 2y = 3x

- Divide both sides by 2

∴ y = 1.5x ⇒ (2)

Now we have a system of equations to solve it

Substitute y in equation (1) by equation (2)

∴ x + 5 = 1.5x + 2

- Subtract 1.5x from both sides

∴ - 0.5x + 5 = 2

- Subtract 5 from both sides

∴ - 0.5x = -3

- Divide both sides by - 0.5

∴ x = 6

- Substitute the value of x in equation (2) to find y

∵ y = 1.5(6)

∴ y = 9

The values of x and y are x = 6 and y = 9