Question

8. The measure of an angle of a parallelogram
is double than its adjacent angle. Find
the measure of all its angles​

Answer 1

Answer:

Let the two adjacent angles be x° and 2x° . In a parallelogram, sum of the adjacent angles are 180°. Thus , the two adjacent angles are 120° and 60°. Hence, the angles of the parallelogram are 120°, 60°, 120° and 60°.

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

• The measure of an angle of a parallelogram is double that its adjacent angle.

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The measure of all the angles of the parallelogram.

$\bf{\underline{\underline\green{Solution:-}}}$

As we know that

The opposite sides of the parallelogram are parallel.

The sum of adjacent angles in the parallelogram is 180°

(Because sum of interior allied angles of two parallel lines is 180°)

Given, that the measure of an angle of a parallelogram

is double than its adjacent angle.

So:-

Let one of the angle be x

Then, the angle adjacent to it = 2x

Sum of adjacent angles is 180°

Therefore:-

$\rm\implies2x + x = 180 \degree$

$\rm\implies3x = 180 \degree$

$\rm\implies x = \dfrac{180}{3}$

$\rm\implies x = 60 \degree$

One angle = x = 60°

The adjacent angle = 2 × 60 = 120°

Therefore:-

$\rm\implies \angle A = 60 \degree$

$\rm\implies \angle B = 120 \degree$

As the opposite angles of a parallelogram are equal

⟹∠B = ∠C

$\rm\implies \angle C = 120 \degree$

∠A= ∠D

$\rm\implies \angle D = 60 \degree$