Question

1. The adjacent angles of a parallelogram are in the ratio of
2:3. The measures of the angles are​

Answer 1

Given:

A parallelogram with

• Adjacent angles in ratio = 2:3

What To Find:

We have to find the measures of the angles.

How To Find:

To find the measures of the angles we have to

• Use the property.
• Form a linear equation on it.

Property For Finding:

Sum of Adjacent Angles of Parallelogram = 180°

Solution:

→ Let the common measures be x.

∴ Hence the equation will be with the property,

⇒ 2x + 3x = 180°

Add 2x and 3x,

⇒ 5x = 180°

Take 5 to RHS,

⇒ $\sf x = \dfrac{180}{5}$

Divide 180 by 5,

⇒ x = 36

Now,

Substitute the values in 2x and 3x,

→ 2x = 2 × 36 = 72°

→ 3x = 3 × 36 = 108°

∴ Therefore, the measures of angles of the parallelogram are 72° and 108° respectively.

Answer 2

Given:

A parallelogram with

Adjacent angles in ratio = 2:3

What To Find:

We have to find the measures of the angles.

How To Find:

To find the measures of the angles we have to

Use the property.

Form a linear equation on it.

Property For Finding:

Sum of Adjacent Angles of Parallelogram = 180°

Solution:

→ Let the common measures be x.

∴ Hence the equation will be with the property,

⇒ 2x + 3x = 180°

Add 2x and 3x,

⇒ 5x = 180°

Take 5 to RHS,

⇒ $\sf x = \dfrac{180}{5}$

Divide 180 by 5,

⇒ x = 36

Now,

Substitute the values in 2x and 3x,

→ 2x = 2 × 36 = 72°

→ 3x = 3 × 36 = 108°

∴ Therefore, the measures of angles of the parallelogram are 72° and 108° respectively.