Question

The measure of one interior angle of a parallelogram is 30 degrees more than 2 times the measure of another angle. Find the measure of each angle.

Answer 1

Answer:

        30° and 150°    

Step-by-step explanation:

α   - one angle

2α   - two times measure of angle α

2α + 30°    - second angle

Paralleogram has two pairs of angles of the same measure.

Sum of interior angles of any quadrangle is 360°

Therefore:

2×α + 2×(2α + 30°) = 360°        {divide both sides by 2}

α + 2α + 30° = 180°                 {subtract 30° from both sides}

  3α = 150°                        {divide both sides by 3)

      α = 50°

2α+30° = 2×50° + 30° = 130°