Question

An angle measures 30° less than the measure of its supplementary angle. What is the measure of each angle?

Answer 1

To find the measure of each angle, set up an equation using x as the angle measure and solve for x.

Step-by-step explanation:

To find the measure of each angle, we can set up an equation based on the given information. Let's denote the measure of the angle as x. The measure of its supplementary angle is 180° - x. According to the problem, we have x = 180° - x - 30°.

Simplifying the equation, we get 2x = 150°, which gives us x = 75°.

Therefore, the angle measures 75° and its supplementary angle measures 180° - 75° = 105°.

Answer 2

The measures of each would be:

105° and 75°

Step-by-step explanation:

Supplementary angles are two angles whose measures sum up to 180° or they form a straight line.

So if an angle measures 30° less than the measure of its supplementary, it wold mean that both angles together is equal to 180°.

∠1 = x

∠2 = x-30°

∠1 + ∠2 = 180°

So here we plug in our equations:

∠1 + ∠2 = 180°

x + x - 30° = 180°

2x - 30° = 180°

We solve for the x then:

Add 30° on both sides of the equation:

2x - 30° + 30° = 180° + 30°

2x = 210°

Divide both sides by 2:

2x/2 = 210°/2

x = 105°

∠1 = 105°

Now we solve for the second angle:

∠1 + ∠2 = 180°

105° + ∠2 = 180°

Subtract 105° from both sides of the equation:

105° + ∠2 - 105° = 180° - 105°

∠2 = 75°