Verified answer

Step-by-step explanation:

Let the measures of the two adjacent angles of the parallelogram be 3x and 2x.

We know that, opposite angles of a parallelogram are equal,

So the other adjacent angle in the parallelogram will also be 3x, and the final adjacent angle will be 2x.

Therefore, the measures of all four angles of the parallelogram are 3x, 3x, 2x, and 2x.

The sum of the angles in a parallelogram is 360°. So:

→ 3x + 3x + 2x + 2x = 360

→ 10x = 360

→ x = 36

Therefore, the measures of the two adjacent angles of the parallelogram are:

→ 3x = 3(36) = 108°

→ 2x = 2(36) = 72°

So, the two adjacent angles in the parallelogram measure 108° and 72°, respectively.

Answer :-

• The each of the angles of parallelogram is 108°, 72°.

Given :-

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

To Find :-

• Find the each of the angles of the parallelogram ?

Solution :-

• Let the each angles of parallelogram be 3x and 2x.

Adjacent angles of a parallelogram

➤ 3x + 2x = 180°

➤ 5x = 180°

➤ x = 180°/5

• Cross - multiplication

➤ x = 36°

Angles of the parallelogram

• 3x° = (3 × 36)° = 108°
• 2x° = (2 × 36)° = 72°

Hence,

• The each of the angles of parallelogram is 108°, 72°.

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Verification :-

➤ 3x + 2x = 180°

➤ (3 × 36) + (2 × 36) = 180°

➤ 108 + 72 = 180°

➤ 180° = 180°

• LHS = RHS