1. The measure of two adjacent angles of a parallelogram is in the ratio 4:2. Find the measure of each of the angles of the parallelogram.

Question

1. The measure of two adjacent angles of a parallelogram is in the ratio 4:2. Find the measure of each of the angles of the parallelogram.

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3 weeks 2021-09-05T06:59:20+00:00 2 Answers 0 views 0

Given:

Ratio of two adjacent angles of a parallelogram = 4 : 2.

Let the measures of angles be 4x , 2x.

We know that,

Sum of two adjacent angles of a parallelogram = 180°

Hence,

→ 4x + 2x = 180°

→ 6x = 180°

→ x = 180/6

→ x = 30

Hence,

• 1st angle = 4x = 4(30) = 120°
• 2nd angle = 2x = 2(30) = 60°.

We know,

Opposite angles of a parallelogram are equal.

so, the measures of other two angles are also 120° , 60°.

Therefore, the measures of four angles of the given parallelogram are 120° , 60° , 120° , 60°.

2. Given:–

• The measure of two adjacent angles of a parallelogram is in the ratio 4:2.

ToFind:–

• Measure of each of the angles of the parallelogram.

Solution:–

☯️ We know that,

Sum Of Adjacent Angles = 180°

Now,

Let the angles be 4x, 2x.

Put the values.

⇒ 4x + 2x = 180°

⇒ 6x = 180°

⇒ x = 180/6.

⇒ x = 30.

Hence,

• 1st Angle = 4x = 120°
• 2nd Angle = 3x = 60°
• 3rd Angle = 120°
• 4th Angle = 60°

Opposite Angles Of a Parallelogram are equal. So, 3rd and 4th Angle will become 120° and 60°.