Question

Find the value of x, y, and z in the parallelogram below.

P=
y =
11
(-y-1)⁰
119⁰
(-4x-5)
(-10z+1)

Answer 1

`\boxed{x = -31}`

`\boxed{y = -62}`

`\boxed{z = -6}}`

Explanation:

There are a couple of properties of parallelograms that can help solve for the unknowns

1. The opposite angles of a parallelogram are congruent(equal)
2. Consecutive angles are supplementary(add up to 180°)

Using property 1 that opposite angles are equal we have:
-4x - 5 = 119

⇒ -4x = 119 + 5

⇒ -4x = 124

⇒ x = 124/-4

⇒ x = -31

Using property 2 that consecutive angles are supplementary on angles
(-y - 1)° and 119°:

(- y - 1) + 119 = 180

⇒ - y - 1 + 119 = 180

⇒ - y + 118 = 180

⇒ - y = 180 - 118

⇒ - y = 62

⇒ y = -62

Using property 2 for angles (-10z - 1)° and 119°
(-10z + 1) + 119 = 180

- 10z + 1 + 119 = 180

⇒ - 10z + 120 = 180

⇒ -10z = 180 - 120

⇒ -10z = 60

⇒ z = 60/-10

⇒ z = -6