Question

Two angles are supplementary . The measure of one angle exceeds three times the measure of the other angle by 32. What is the degree measure of the smaller angle?

Answer 1

Let the two angles be 'x' and 'y'.

Since, the angles are supplementary.

When the angles are supplementary, then the sum of the measures of the angles is 180 degrees.

`x + y = 180^\circ` (Equation 1)

Since, the measure of one angle exceeds three times the measure of the other angle by 32.

`x = (3 * y) + 32`

`x = 3y + 32`

Substituting the value of 'x' in equation 1, we get

`x+ y = 180^\circ`

`3y+32+ y = 180^\circ`

`4y+32 = 180^\circ`

`4y= 180-32`

`4y = 148^\circ`

y =
`37^\circ`

So, the measure of the smaller angle is
`37^\circ`.