Question

two angles are complementary. the measure of the larger angle is 6° less than 3 times the measure of the smaller angle. the measure of the smaller angle is _ degrees and the measure of the larger angle is _ degrees.

Explanation:

Step1: Define variables

Let the measure of the smaller angle be $x$ degrees. Then the measure of the larger angle is $(3x - 6)$ degrees.

Step2: Use the complementary - angle property

Since the two angles are complementary, their sum is $90^{\circ}$. So we have the equation $x+(3x - 6)=90$.

Step3: Simplify the equation

Combine like - terms: $x + 3x-6=90$, which simplifies to $4x-6 = 90$.

Step4: Solve for $x$

Add 6 to both sides of the equation: $4x-6 + 6=90 + 6$, getting $4x=96$. Then divide both sides by 4: $x=\frac{96}{4}=24$.

Step5: Find the measure of the larger angle

Substitute $x = 24$ into the expression for the larger angle $3x-6$. So the larger angle is $3\times24-6=72 - 6=66$ degrees.

Answer:

The measure of the smaller angle is 24 degrees and the measure of the larger angle is 66 degrees.