The measures of the angles are: First angle: 42 degrees
Second angle: 48 degrees .
Finding the Measures of Complementary Angles:
Step 1: Define variables:
Let x be the measure of one angle.
Therefore, the measure of the other angle is x + 6 (6 more than the first angle).
Step 2: Apply the complementary relationship:
Since the angles are complementary, their sum is equal to 90 degrees.
So, we can set up an equation:
x + (x + 6) = 90
Step 3: Solve for x:
Combine like terms:
2x + 6 = 90
Subtract 6 from both sides:
2x = 84
Divide both sides by 2:
x = 42
Step 4: Find the measure of the other angle:
Substitute x back into the expression for the other angle:
x + 6 = 42 + 6 = 48
Therefore, the measures of the angles are:
First angle: 42 degrees
Second angle: 48 degrees