The ratio of two supplementary angles is 4: 1, find the measures of both angles.

The measures of both the angles are 36 degrees and 144 degrees and this can be determined by using the concept of supplementary angles.

Given :

The ratio of two supplementary angles is 4:1.

The following steps can be used in order to determine the measures of both angles:

Step 1 - The concept of supplementary angles is used in order to determine the measures of both angles.

Step 2 - When two angles are supplementary, then their sum is 180 degrees.

Step 3 - Let the one angle be 'x' then another angle is 4x.

Step 4 - So, the value of 'x' can be calculated as:

x + 4x = 180

5x = 180

x = 36 degrees

Step 5 - Therefore, the measure of another angle is 144 degrees.

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