Question

the sum of the measures of the angles of a parallelogram is 360 degrees. in the parallelogram on the right, angles a and d have the same measures as well as angles c and b. if the measures of angle c is nine times the measure of angle a, find the measure of each angle.

Answer 1

∠A=18°

∠B=162°

∠C=162°

∠D=18°

Explanation:

we know that

∠A+∠B+∠C+∠D=360° ----> equation A

∠A=∠D ----> equation B

∠C=∠B ----> equation C

∠C=9∠A ----> equation D

step 1

substitute equation B and equation C in equation A

∠A+∠C+∠C+∠A=360°

2∠A+2∠C=360° ----> equation E

step 2

Find the measure of angle A

substitute equation D in equation E

2∠A+2(9∠A)=360°

2∠A+18∠A=360°

20∠A=360°

∠A=18°

step 3

Find the measure of angle C (equation D)

∠C=9(18°)=162°

therefore

∠A=18°

∠B=162°

∠C=162°

∠D=18°