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.

$x = (3 \times y) + 32$

$x = 3y + 32$

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  $37^\circ$.