In ANOP, NP is extended through point P to point Q, m_OPQ = (9x – 19)°, mZPNO = (2x + 5), and mZNOP = (3x + 16º. Find mZNOP.

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

The insurance company has a good reason to be concerned with the possibilities of plumbing problems (B), overflowed drainage (C), or fire (D).  If any of these things happens, the insurance company will be expected to cover a big part of the expense.

But the likelihood of remodeling (A) is none of their business.  Remodeling happens when the owner decides.  It's not accidental or unexpected.  And when it happens, the owner pays for it, and the insurance company is not on the hook.  Remodeling should have no effect whatsoever on the homeowner's insurance premium.