Question

Send help! Let angle 1 and angle 2 be complementary angles, and let angle 2 and angle 3 be supplementary angles. If angle 1 = x and angle 2 = 2x, determine x. Then find angle 1, angle 2, and angle 3.

Answer 1

1. x = 30

2. ∠1 = 30°

3. ∠2 = 60°

4. ∠3 = 120°

Explanation:

⭐What are supplementary angles?

• two or more angles that add up to 180°

⭐What are complementary angles?

• two or more angles that add up to 90°

Set up the equations for the situation:

∠1 + ∠2 = 90

∠2 + ∠3 = 180

x + 2x = 90 . . . (1)

2x + ∠3 = 180 . . . (2)

First, solve for "x" in equation 1:

x + 2x = 90

3x = 90

∴ x = 30

Next, substitute "x" into ∠1 and ∠2 to solve for ∠1 and ∠2:

∠1 = x

∴ ∠1 = 30°

∠2 = 2x

∠2 = 2(30)

∴ ∠2 = 60°

Finally, substitute "x" into equation 2 to solve for ∠3:

2x + ∠3 = 180

2(30) + ∠3 = 180

60 + ∠3 = 180

∴ ∠3 = 120°