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Question

Difficulty: MediumLines and Angles

Two angles are supplementary. The measure of the larger angle is 24∘24^\circ more than three times the measure of the smaller angle. What is the measure, in degrees, of the larger angle?

Answer: 141 degrees

Answer

141
Supplementary angles have a total sum of 180∘180^\circ. By letting the smaller angle equal xx, the larger angle becomes 3x+243x + 24. Adding these gives x+(3x+24)=180x + (3x + 24) = 180. Simplifying this results in 4x=1564x = 156, so x=39x = 39. Since the question asks for the larger angle, we must substitute x=39x = 39 into our expression for the larger angle: 3(39)+24=117+24=1413(39) + 24 = 117 + 24 = 141. Therefore, the larger angle measures 141∘141^\circ.

Step-by-Step Solution

1
Assign algebraic expressions to the unknown angles.
Smaller angle = xx, Larger angle = 3x+243x + 24
This translates the given text relationships into mathematical variables that can be used to set up an equation.
2
Set up an equation based on the geometric property of supplementary angles.
x+(3x+24)=180x + (3x + 24) = 180
Supplementary angles, by definition, always add up to exactly 180 degrees.
3
Simplify and solve the linear equation for xx.
4x=1564x = 156, meaning x=39x = 39
Isolating xx provides the measure of the smaller angle.
4
Calculate the measure of the larger angle.
3(39)+24=1413(39) + 24 = 141
The question specifically asks for the measure of the larger angle, so we must plug xx back into the original expression.

Key Concept

Solving algebraic equations involving supplementary angles
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Topics

Lines and Angles

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