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If angle A and angle B are supplementary, and angle A is 3 times angle B, what i

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Question: If angle A and angle B are supplementary, and angle A is 3 times angle B, what is the measure of angle A?

Options:

  1. 90 degrees
  2. 120 degrees
  3. 180 degrees
  4. 60 degrees

Correct Answer: 120 degrees

Solution: 

Let angle B be x. Then angle A = 3x. Since they are supplementary, x + 3x = 180, leading to 4x = 180, so x = 45. Therefore, angle A = 3 * 45 = 135 degrees.

If angle A and angle B are supplementary, and angle A is 3 times angle B, what i

Practice Questions

Q1
If angle A and angle B are supplementary, and angle A is 3 times angle B, what is the measure of angle A?
  1. 90 degrees
  2. 120 degrees
  3. 180 degrees
  4. 60 degrees

Questions & Step-by-Step Solutions

If angle A and angle B are supplementary, and angle A is 3 times angle B, what is the measure of angle A?
  • Step 1: Understand that supplementary angles add up to 180 degrees.
  • Step 2: Let angle B be represented as 'x'.
  • Step 3: Since angle A is 3 times angle B, write angle A as '3x'.
  • Step 4: Set up the equation for supplementary angles: x + 3x = 180.
  • Step 5: Combine like terms: 4x = 180.
  • Step 6: Solve for x by dividing both sides by 4: x = 180 / 4.
  • Step 7: Calculate x: x = 45 degrees (this is angle B).
  • Step 8: Find angle A by multiplying angle B by 3: angle A = 3 * 45.
  • Step 9: Calculate angle A: angle A = 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.
  • Proportional Relationships – Understanding the relationship between angles when one is a multiple of the other.
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