Question

In a parallelogram WXYZ , W and X are adjacent interior angles the measure of X is three times the measure of W which equation gives the exact measure of W

Answer 1

The required equation is
`\angle W+3\angle W=180^(\circ)`.

Explanation:

Given information: WXYZ is a parallelogram, W and X are adjacent interior angles and measure of X is three times the measure of W.

According to the properties of parallelogram, the two adjacent interior angle are supplementary angle and their sum is 180 degrees.

`\angle W+\angle X=180^(\circ)` .... (1)

It is also given that the measure of X is three times the measure of W.

`\angle X=3\angle W`

Substitute this value in equation 1.

`\angle W+3\angle W=180^(\circ)`

`4\angle W=180^(\circ)`

`\angle W=45^(\circ)`

Substitute this value in equation 1.

`\angle W=135^(\circ)`

Therefore the required equation is
`\angle W+3\angle W=180^(\circ)`.