Answer :

›»› The measure of all angles of the parallelogram is 60°, 120°, 60°, and 120°.

Given :

• The ratio of MEASURES of two adjacent angles of a parallelogram is 1:2.

To Find :

• The measures of all angles of the parallelogram.

Solution :

Let US assume that, the measures of two adjacent angles of a parallelogram is "1x" and "2x" respectively.

As we know that

The sum of adjacent angle of parallelogram is 180°.

→ 1x + 2x = 180

→ x + 2x = 180

→ 3x = 180

→ x = 180 ÷ 3

→ x = 60

Therefore,

The measure of two adjacent angle of parallel will be,

• 1x = 1 * 60 = 60°.
• 2x = 2 * 60 = 120°.

As we know that

The OPPOSITE angles of parallelogram are equal and parallel.

So, Opposite angle of 60° is 60°

And, Opposite angle of 120° is also 120°.

Hence, the measure of all angles of the parallelogram is 60°, 120° 60°, and 120°.

Verification :

The sum of all FOUR angles of a parallelogram is 360°.

→ 60 + 120 + 60 + 120 = 360

→ 180 + 60 + 120 = 360

→ 180 + 180 = 360

→ 360 = 360

Clearly, LHS = RHS

Here, both the conditions satisfy, so our answer is correct.

Hence Verified !