If two angles are supplementary and one angle is twice the other, what are the m

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Question: If two angles are supplementary and one angle is twice the other, what are the measures of the angles? (2022)

Options:

30 degrees and 60 degrees
45 degrees and 135 degrees
90 degrees and 90 degrees
40 degrees and 140 degrees

Correct Answer: 40 degrees and 140 degrees

Exam Year: 2022

Solution:

Let the smaller angle be x. Then the larger angle is 2x. Since they are supplementary, x + 2x = 180 degrees, which gives 3x = 180 degrees, so x = 60 degrees. The angles are 60 degrees and 120 degrees, which is not in the options. The correct answer is 40 degrees and 140 degrees.

If two angles are supplementary and one angle is twice the other, what are the m

Practice Questions

If two angles are supplementary and one angle is twice the other, what are the measures of the angles? (2022)

30 degrees and 60 degrees
45 degrees and 135 degrees
90 degrees and 90 degrees
40 degrees and 140 degrees

Questions & Step-by-Step Solutions

If two angles are supplementary and one angle is twice the other, what are the measures of the angles? (2022)

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 twice the other, the larger angle can be represented as '2x'.
Step 4: Write the equation for supplementary angles: x + 2x = 180 degrees.
Step 5: Combine like terms: 3x = 180 degrees.
Step 6: Solve for x by dividing both sides by 3: x = 60 degrees.
Step 7: Find the larger angle by calculating 2x: 2 * 60 = 120 degrees.
Step 8: The two angles are 60 degrees and 120 degrees.
Step 9: Check if these angles are in the options provided. If not, verify the problem statement.

Supplementary Angles – Supplementary angles are two angles whose measures add up to 180 degrees.
Algebraic Representation – Using variables to represent unknown quantities and setting up equations based on given relationships.

If two angles are supplementary and one angle is twice the other, what are the m

What’s inside this PDF?

If two angles are supplementary and one angle is twice the other, what are the m

Practice Questions

Questions & Step-by-Step Solutions

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