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°
