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 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 $3x - 14$ degrees.

Step2: Use the complementary - angle property

Since the two angles are complementary, their sum is 90 degrees. So, $x+(3x - 14)=90$.

Step3: Simplify the equation

Combine like - terms: $x + 3x-14=90$ becomes $4x-14 = 90$.

Step4: Solve for $x$

Add 14 to both sides of the equation: $4x-14 + 14=90 + 14$, which gives $4x=104$. Then divide both sides by 4: $x=\frac{104}{4}=26$.

Step5: Find the measure of the larger angle

Substitute $x = 26$ into the expression for the larger angle: $3x-14=3\times26-14=78 - 14 = 64$.

Answer:

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