Question

The measure of one interior angle of a parallelogram is 30° more than two

times the measure of another angle. Find the measure of each angle of the
parallelogram.

Answer 1

The measure of one interior angle is 130°

The measure of other interior angle is 50° .

Explanation:

Given as :

The measure of one interior angle of a parallelogram is 30° more than two

times the measure of another angle.

Let The measure of one interior angle = x°

And The measure of other interior angle = y°

∵ Interior angle on same side of transversal are supplementary

So, ∠x + ∠y = 180° .........A

And according to question

∠x = 2×∠y + 30° ...........B

Solving eq A and eq B

2×∠y + 30° + ∠y = 180°

Or, 3×∠y = 180° - 30°

Or, 3×∠y = 150°

∴ ∠y =
`(150)/(3)`

i.e ∠y = 50°

So, The measure of other interior angle = ∠y = 50°

Put the value of ∠y in eq B

∵ ∠x = 2×∠y + 30°

Or, ∠x = 2×50° + 30°

Or, ∠x = 100° + 30°

i.e ∠x = 130°

So, The measure of one interior angle = ∠x = 130°

Hence, The measure of one interior angle is 130° and The measure of other interior angle is 50° . Answer