Question

The deck that Kenneth is building is the shape of a parallelogram, ABCD. The measure of angle C is one-third the measure of angle B. Find the measure of each angle of the deck.

Answer 1

A = 45°, B = 135°, C = 45° and D = 135°,

Explanation:

Kenneth building is in the shape of a parallelogram, ABCD.

Since, opposite angles of a parallelogram are equal,

A = C and B = D. --- (1)

Since, adjacent angles of a parallelogram are supplementary,

B + C = 180 --- (2)

But, it is given that the measure of angle C is one third of measure of angle B.

Therefore,
`C = (1)/(3) (B)` or

B = 3C

Substitute in (2), we get,

3C + C = 180

4C = 180

Divide both sides by 4.

C = 45°

B + C = 180

B + 45 = 180

B = 180 - 45

B = 135°

From (1),

A = C and B = D

Therefore, A = 45° and D = 135°

Hence, A = 45°, B = 135°, C = 45° and D = 135°,