Final answer:
The measure of each angle is obtained by setting up an equation where one angle is x and the other is x + 26°. Solving this equation, we find out that the first angle is 32° and its complementary angle is 58°.
Step-by-step explanation:
To find the measure of each angle when one angle measures 26° more than its complementary angle, we use the concept of complementary angles. Complementary angles are two angles whose sum is 90°. Let the measure of the first angle be x, so the measure of its complementary angle would be x + 26°.
To find the values of both angles, we set up the equation:
x + (x + 26°) = 90°
Which simplifies to:
2x + 26° = 90°
Subtracting 26° from both sides gives us:
2x = 64°
Dividing both sides by 2 to find the value of x results in:
x = 32°
So, the first angle measures 32° and its complementary angle, being 26° more, measures 58°.