Question

Figure PQRS is a parallelogram. The expressions represent the measures of the angles in degrees.

Parallelogram P Q R S is shown. Angle Q is (20 + 2 x) degrees and angle R is (6x) degrees.

What is the value of x?

5
10
20
25

Answer 1

c

Explanation:

Answer 2

Given:

In parallelogram PQRS,
`m\angle Q=(20+2x)^\circ,\ m\angle R=6x^\circ`.

To find:

The value of x.

Solution:

In a parallelogram, the consecutive interior angles are supplementary angles.

In parallelogram PQRS,

`m\angle Q+m\angle R=180^\circ` (Supplementary angles)

`(20+2x)^\circ+(6x)^\circ=180^\circ`

`(20+8x)^\circ=180^\circ`

`20+8x=180`

Subtracting 20 from both sides, we get

`8x=180-20`

`8x=160`

Divide both sides by 8.

`(8x)/(8)=(160)/(8)`

`x=20`

Therefore, the correct option is C.