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

The angles of the deck are 45°, 135°, 45° and 135°.

Explanation:

It is given that C is one third of measure of angle B.

But, in a parallelogram, adjacent angles are supplementary.

Therefore, B + C = 180

`C=(1)/(3) B`

`B=(B)/(3) =180`

`(4B)/(3) =180`

`B=180((3)/(4) )`

B = 135

and
`C=(135)/(3)`

C = 45

Since, opposite angles are equal in a parallelogram,

A = C = 45 and

D = B = 135

Hence, the angles of the deck are 45°, 135°, 45° and 135°.