Question

two angles are supplementary. the measure of the larger angle is 12 less than 3 times the measure of the smaller angle. find the measure of the larger angle. a) 25.5° b) 64.5° c) 132° d) 144°

Explanation:

Step1: Let the measure of the smaller angle be $x$.

The measure of the larger angle is $3x - 12$.

Step2: Use the property of supplementary angles.

Since the two angles are supplementary, $x+(3x - 12)=180$.

Step3: Simplify the equation.

Combine like - terms: $4x-12 = 180$.
Add 12 to both sides: $4x=180 + 12=192$.

Step4: Solve for $x$.

Divide both sides by 4: $x=\frac{192}{4}=48$.

Step5: Find the measure of the larger angle.

Substitute $x = 48$ into the expression for the larger angle: $3x-12=3\times48-12=144 - 12=132$.

Answer:

C. $132^{\circ}$