Question

5. 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 .
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Answer 1

Step-by-step explanation:

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Answer 2

Answer :

›»› The measure of each of the angles of the parallelogram are 108°, 72°, 108° and 72°.

Given :

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

To Find :

• The measure of each of the angles of the parallelogram.

Solution :

Let,

The measure of two adjacent angle be "3x" and "2x" respectively.

As we know that

The sum of the measure of adjacent angle is 180°.

→ 3x + 2x = 180

→ 5x = 180

→ x = 180/5

→ x = 36

Therefore,

→ The measure of first angle = 3x

→ The measure of first angle = 3 * 36

→ The measure of first angle = 108°

→ The measure of second angle = 2x

→ The measure of second angle = 2 * 36

→ The measure of second angle = 72°

→ First angle = third angle (Opposite angles).

→ Second angle = fourth angle (Opposite angles).

→ 108° = 108° (Opposite angles).

→ 72° = 72° (Opposite angles).

║Hence the measure of each of the angles of the parallelogram are 108°, 72°, 108° and 72°.║

Verification :

Sum of all angles of parallelogram is 360°

→ 108 + 72 + 108 + 72 = 360

→ 180 + 108 + 72 = 360

→ 180 + 180 = 360

→ 360 = 360

Here, LHS = RHS

Hence Verified !