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

Respuesta :

Given:

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

To find:

The value of x.

Solution:

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

In parallelogram PQRS,

[tex]m\angle Q+m\angle R=180^\circ[/tex]            (Supplementary angles)

[tex](20+2x)^\circ+(6x)^\circ=180^\circ[/tex]

[tex](20+8x)^\circ=180^\circ[/tex]

[tex]20+8x=180[/tex]

Subtracting 20 from both sides, we get

[tex]8x=180-20[/tex]

[tex]8x=160[/tex]

Divide both sides by 8.

[tex]\dfrac{8x}{8}=\dfrac{160}{8}[/tex]

[tex]x=20[/tex]

Therefore, the correct option is C.

Answer:

c

Step-by-step explanation:

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