Question

The sum of the measures of the angles of a parallelogram is​ 360°. In the parallelogram on the​ right, angles A and D have the same measure as well as angles C and B. If the measure of angle C is eight timeseight times the measure of angle​ A, find the measure of each angle.

Answer 1

Answer: The angles measure A = 20 degrees, B= 160 degrees, C = 160 degrees and D = 20 degrees.

Step-by-step explanation: One of the properties of a parallelogram is that opposite angles are equal. Hence we are given that angles A and D have the same measurement. Angles C and B also have the same measurement since they are also opposite each other. If angle C is eight times angle A, then angle C can be expressed as 8A, and the same applies to angle B. So, the four angles can be expressed as;

A + A + 8A + 8A = 360

(The sum of the four angles in a parallelogram equals 360 degrees)

2A + 16A = 360

18A = 360

Divide both sides of the equation by 18

A = 20

Therefore angle A = 20 and angle D = 20

Angle B = 160 and angle C = 160

Answer 2

A = 20 degree

B = 160 degree

C = 160 degree

D = 20 degree

Explanation:

If the measure of angle C is eight timeseight times the measure of angle​ A

That means C = 8A

But According to the question, angles A and D have the same measure as well as angles C and B.

That is, B = 8A and D = A

If A + B + C + D = 360

Let us substitute for B, C and D

A + 8A + 8A + A = 360

18A = 360

A = 360/18 = 20

Therefore

A = 20 degree

B = 8 × 20 = 160 degree

C = 8× 20 = 160 degree

D = 20 degree