Question

The measures of two adjacent angles of a parallelogram are in the ratio 3 : 2. Find the measure of each of the angles of the parallelogram​

Answer 1

Answer:

Given :-

• The measure of two adjacent angles of a parallelogram are in the ratio of 3 : 2.

To Find :-

• What is the measure of each of the angles of the parallelogram.

Solution :-

Let,

➲ First Angle Of Parallelogram = 3x

➲ Second Angle Of Parallelogram = 2x

As we know that :

$\footnotesize\bigstar\: \: \sf\boxed{\bold{\pink{Sum\: of\: all\: measure\: of\: adjacent\: angles =\: 180^{\circ}}}}\: \: \bigstar$

According to the question by using the formula we get,

$\implies \sf 3x + 2x =\: 180^{\circ}$

$\implies \sf 5x =\: 180^{\circ}$

$\implies \sf x =\: \dfrac{180^{\circ}}{5}$

$\implies \sf\bold{\purple{x =\: 36^{\circ}}}$

Hence, the required measure of each of the angles of the parallelogram are :

❒ First Angle Of Parallelogram :

⇒ First Angle = 3x

⇒ First Angle = 3(36°)

⇒ First Angle = 3 × 36°

➠ First Angle = 108° (Opposite Angles)

❒ Second Angle Of Parallelogram :

⇒ Second Angle = 2x

⇒ Second Angle = 2(36°)

⇒ Second Angle = 2 × 36°

➠ Second Angle = 72° (Opposite Angles)

Since, the opposite angles are equal in a parallelogram.

∴ The measure of each of the angles of the parallelogram are 108°, 72°, 108° and 72° respectively.