Question

two angles are complementary. the measure of the larger angle is 14° less than 3 times the measure of the smaller angle. the measure of the smaller angle is 26 degrees and the measure of the larger angle is 64 degrees.

Explanation:

Step1: Define variables

Let the measure of the smaller angle be $x$ degrees and the measure of the larger angle be $y$ degrees.

Step2: Set up equations

Since the two angles are complementary, $x + y=90$. Also, given that $y = 3x-14$.

Step3: Substitute and solve

Substitute $y = 3x - 14$ into $x + y=90$. We get $x+(3x - 14)=90$. Combine like - terms: $4x-14 = 90$. Add 14 to both sides: $4x=90 + 14=104$. Divide both sides by 4: $x=\frac{104}{4}=26$.

Step4: Find the larger angle

Substitute $x = 26$ into $y = 3x-14$. Then $y=3\times26-14=78 - 14=64$.

Answer:

The measure of the smaller angle is 26 degrees and the measure of the larger angle is 64 degrees.