Question

The supplement of an angle is twice the meausurement of the angle. Find the measurement of the smaller angle

Answer 1

60° and 120°

Explanation:

Supplementary angles are 2 angles that add up to 180°

From the given information we can write 2 equations...

1) It mentions supplement, so we can say

a + b = 180° (a is the angle, b is the supplement)

2) "The supplement of an angle is twice the measurement of the angle",

Since b is the supplement,

b = 2a

We can substitute equation to into the first equation and solve

a + 2a = 180° (b becomes 2a)

3a = 180° (combine like terms)

a = 60° (divide both sides by 3 to isolate a)

Since a + b = 180°, and a = 60°, solve..

60° + b = 180°

b = 120° (subtract 60° from both sides to isolate b)

Answer 2

Hello from MrBillDoesMath!

Answer:

60

Discussion:

Let the angle be @. The supplement of the angle is 180 - @ and we are told it equals 2@. That is,

180 -@ = 2@ => add @ to both sides

180 = 2@ +@ => 2@ +@ = 3@

180 = 3@ => divide both sides by 3

180/3 = @

@ = 60

Check: the supplement of an angle (which is 180 - @ - 180 -60 = 120) is twice the measure of the angle (@ = 60 and 2@ = 120). Indeed, they agree.

Thank you,

MrB