If one angle of a parallelogram is 12° less than twice the smallest angle of the same parallelogram, then the largest angle of the parallelogram is:

Correct option is A

Given:

One angle of a parallelogram is 12° less than twice the smallest angle.

Concept Used:

Adjacent angles are supplementary (sum to 180°).

Solution:

Let the smallest angle of the parallelogram be 'x' degrees.

Then, the other angle is (2x - 12) degrees.

The sum of adjacent angles in a parallelogram is 180°.

x + (2x - 12) = 180

3x - 12 = 180

3x = 180 + 12

3x = 192

x = 64

2x - 12 = 2(64) - 12

2x - 12 = 128 - 12

2x - 12 = 116

The angles of the parallelogram are 64° and 116°.

The largest angle is 116°.

Therefore, the largest angle of the parallelogram is 116°.

Alternate Solution:

Let the smaller angle be 'x'.

The larger angle is '2x - 12'.

Since adjacent angles are supplementary, x + 2x - 12 = 180.

3x - 12 = 180.

3x = 192.

x = 64.

The larger angle is 2(64) - 12 = 128 - 12 = 116.

The largest angle is 116 degrees.