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

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.

$\dfrac{8x}{8}=\dfrac{160}{8}$

$x=20$

Therefore, the correct option is C.

Answer 2

Answer:

c

Step-by-step explanation: