Question

1. for two supplementary angles, the measure of the larger angle is five times larger than the measure of the smaller angle. find the measure of the larger angle. justify how you found your answer.

Explanation:

Step1: Define variables

Let the measure of the smaller angle be $x$. Then the measure of the larger angle is $5x$.

Step2: Use the supplementary - angle property

Since the two angles are supplementary, their sum is $180^{\circ}$. So, $x + 5x=180$.

Step3: Solve the equation

Combining like - terms, we get $6x = 180$. Dividing both sides by 6, we have $x=\frac{180}{6}=30$.

Step4: Find the measure of the larger angle

Substitute $x = 30$ into the expression for the larger angle. The larger angle is $5x$, so $5\times30 = 150^{\circ}$.

Answer:

$150^{\circ}$