Final answer:
To find the measure of the smaller angle in a ratio of 4:5 for two supplementary angles, set up the equation 4x + 5x = 180 and solve for x. The measure of the smaller angle can be found by multiplying x by the ratio.
Step-by-step explanation:
The ratio of the measures of two supplementary angles is 4:5. To find the measure of the smaller angle, we need to determine the value of x. Since the angles are supplementary, their measures add up to 180 degrees. Let's set up the equation:
4x + 5x = 180
Combining like terms, we get 9x = 180. Dividing both sides by 9, we find that x = 20.
Therefore, the measure of the smaller angle is 4x = 4(20) = 80 degrees.