Question

In parallelogram ABCD the degree measure of ABC is 5 times the degree measure of BCD. How many degrees are in the measure of ADC

Answer 1

The measure of ∠ADC is 150°

Explanation:

A parallelogram is a quadrilateral having parallel sides

The basic principle in solving this problem is knowing that opposite angles are congruent meaning they are equal.

Please check attachment for diagrammatic representation.

Now, we have represented ∠BCD by x°, what this means is that ∠ABC will be 5x°. Also, using the opposite angles are congruent property we raised earlier, ∠CAB will be x° while ∠ADC will be 5x°

To get the value of x, the parallelogram property we will be using is that the sum of the interior angles in a parallelogram is 360°.

Therefore, adding all these angles together, we have;

x + x + 5x + 5x + 360

12x = 360

x = 360/12

x = 30°

The measure of ∠ADC is 5x which is 5 × 30 = 150°