If two angles are supplementary and one angle is three times the other, what are

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Question: If two angles are supplementary and one angle is three times the other, what are the measures of the angles?

Options:

Correct Answer: 60 degrees and 120 degrees

Solution:

Let the angles be x and 3x. Then, x + 3x = 180. Solving gives x = 45 degrees and 3x = 135 degrees.

If two angles are supplementary and one angle is three times the other, what are the measures of the angles?

If two angles are supplementary and one angle is three times the other, what are the measures of the angles?

Step 1: Understand that supplementary angles add up to 180 degrees.
Step 2: Let the smaller angle be represented as 'x'.
Step 3: Since one angle is three times the other, represent the larger angle as '3x'.
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 by 4: x = 180 / 4.
Step 7: Calculate x: x = 45 degrees.
Step 8: Find the larger angle by calculating 3x: 3x = 3 * 45 = 135 degrees.
Step 9: Conclude that the two angles are 45 degrees and 135 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 in an equation through algebraic manipulation.