Question

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

Answer 1

Answer:

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°