Two adjacent angles of a parallelogram are in the ratio 4:5 the measure of each of its angles are

Solution:

Given that the adjacent angles of a parallelogram are in the ratio 3:2.

Thus, the angles are 3x and 2x respectively.

We know that the sum of the measures of adjacent angles is 180° for a parallelogram.

∠A + ∠B = 180°

3x + 2x = 180°

5x = 180°

x = 180°/5

x = 36°

Thus, one of the angles = 3x

3(36°) = 108°

The other angle is 2x

2(36°) = 72°

The other two angles are 72° and 108° since opposite angles of a parallelogram are equal.

Thus, the measures of the angles of the parallelogram are 108°, 72°, 108°, and 72°

☛ Check: NCERT Solutions for Class 8 Maths Chapter 3

Video Solution:

NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.3 Question 5

Summary:

The measures of two adjacent angles of a parallelogram are in the ratio 3:2. The measures of each of the angles of the parallelogram are 108°, 72°, 108°, and 72°

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Two adjacent angles of a parallelogram are in the ratio 4: 5 . Find the measure of each of its angles.

Solution

The ratio between two adjacent angles of a || gm ABCD are in the ratio 4 : 5

Let $\angle A=4xand\angle B=5x$

But $\angle A+\angle B={180}^{\circ }$

$\Rightarrow 4x+5x={180}^{\circ }$

$\Rightarrow 9x={180}^{\circ }$

$\therefore x=\frac{{180}^{\circ }}{9}={20}^{\circ }$

$\therefore \angle A=4x=4\times {20}^{\circ }={80}^{\circ }$

$\angle B=5x=5\times 20={100}^{\circ }$

Mathematics

Secondary School Mathematics VIII

Standard VIII