Question

an angle measures 26° more than the measure of its complementary angle. what is the measure of each angle?

Explanation:

Step1: Define complementary angles

Complementary angles add up to 90°. Let the measure of the complementary - angle be $x$. Then the measure of the given angle is $x + 26^{\circ}$.

Step2: Set up an equation

$x+(x + 26^{\circ})=90^{\circ}$.

Step3: Simplify the equation

$2x+26^{\circ}=90^{\circ}$.

Step4: Solve for $x$

Subtract 26° from both sides: $2x=90^{\circ}-26^{\circ}=64^{\circ}$. Then divide both sides by 2: $x = 32^{\circ}$.

Step5: Find the measure of the other angle

The other angle is $x + 26^{\circ}=32^{\circ}+26^{\circ}=58^{\circ}$.

Answer:

58, 32