Question

1. the measure of an angle is 2 more than 3 times its supplement. find the measure of both angles. 3x + 2 = 180

Explanation:

Step1: Let the measure of the angle be $x$ and its supplement be $180 - x$.

Set up the equation based on the problem: $x=3(180 - x)+2$.

Step2: Expand the right - hand side.

$x = 540-3x + 2$.

Step3: Add $3x$ to both sides.

$x+3x=540 + 2$, which simplifies to $4x=542$.

Step4: Solve for $x$.

$x=\frac{542}{4}=135.5$.

Step5: Find the measure of the supplement.

The supplement is $180 - 135.5 = 44.5$.

Answer:

The measure of the angle is $135.5^{\circ}$ and the measure of its supplement is $44.5^{\circ}$