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

What is the value of x?
a.5
b.10
c.20
d.25

Figure PQRS is a parallelogram The expressions represent the measures of the angles in degrees What is the value of x a5 b10 c20 d25 class=

Respuesta :

calculista

we know that

In a parallelogram consecutive angles are supplementary

In this problem

Angle Q and Angle R are consecutive angles

so

[tex](6x)\°+(20+2x)\°=180\°[/tex]

Solve for x

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

[tex]8x=160[/tex]

[tex]x=20\°[/tex]

therefore

the answer is the option C

[tex]x=20\°[/tex]

The sum of the opposite sides of a parallelogram is equal to 180 degrees.

The value of x is 20.

Given

Figure PQRS is a parallelogram.

The expressions represent the measures of the angles in degrees.

What is the property of a parallelogram to calculate the angles?

The sum of the opposite sides of a parallelogram is equal to 180 degrees.

The opposite sides of a parallelogram are congruent.

[tex]\rm m\angle 1+ m\angle 2 = 180\\[/tex]

The measurement of angle 1 is (20+2x) degrees.

The measurement of angle 2 is (6x) degrees.

Therefore,

The value of x is,

[tex]\rm m\angle 1+ m\angle 2 = 180\\\\20+2x+6x=180\\\\8x=180-20\\\\8x=160\\\\x=\dfrac{160}{8}\\\\x=20[/tex]

The value of x is 20.

To know more about Parallelogram click the link given below.

https://brainly.com/question/17167464

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