Question

question 1 - 4 (ma.912.gr.1.1) 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: Set up equations

Let the measure of the smaller angle be $x$ degrees and the measure of the larger angle be $y$ degrees. Since the two angles are complementary, $x + y=90$. Also, given that $y = 3x-6$.

Step2: Substitute $y$ into the first - equation

Substitute $y = 3x - 6$ into $x + y=90$, we get $x+(3x - 6)=90$.
Simplify the left - hand side: $x+3x-6 = 4x-6$. So, $4x-6 = 90$.

Step3: Solve for $x$

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

Step4: Solve for $y$

Substitute $x = 24$ into $y = 3x-6$. Then $y=3\times24-6=72 - 6=66$.

Answer:

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