If two angles are supplementary and one angle measures 3 times the other, what i

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Question: If two angles are supplementary and one angle measures 3 times the other, what is the measure of the smaller angle? (2023)

Options:

Correct Answer: 30 degrees

Exam Year: 2023

Solution:

Let the smaller angle be x. Then the larger angle is 3x. Since they are supplementary, x + 3x = 180. Solving gives x = 45 degrees.

If two angles are supplementary and one angle measures 3 times the other, what is the measure of the smaller angle? (2023)

If two angles are supplementary and one angle measures 3 times the other, what is the measure of the smaller angle? (2023)

Step 1: Define the smaller angle as x.
Step 2: Since the larger angle is 3 times the smaller angle, define the larger angle as 3x.
Step 3: Understand that supplementary angles add up to 180 degrees.
Step 4: Write the equation for the sum of the angles: x + 3x = 180.
Step 5: Combine like terms in the equation: 4x = 180.
Step 6: Solve for x by dividing both sides of the equation by 4: x = 180 / 4.
Step 7: Calculate the value of x: x = 45 degrees.
Step 8: Conclude that the smaller angle measures 45 degrees.

Supplementary Angles – Supplementary angles are two angles whose measures add up to 180 degrees.
Algebraic Representation – Using variables to represent unknown quantities and forming equations based on given relationships.
Solving Linear Equations – Finding the value of a variable by isolating it in an equation.