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If two lines intersect and the measures of the angles formed are in the ratio 2:

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Question: If two lines intersect and the measures of the angles formed are in the ratio 2:3, what is the measure of the larger angle?

Options:

  1. 72 degrees
  2. 108 degrees
  3. 60 degrees
  4. 90 degrees

Correct Answer: 108 degrees

Solution: 

Let the angles be 2x and 3x. Since they are supplementary, 2x + 3x = 180 degrees. Thus, 5x = 180 degrees, x = 36 degrees. The larger angle is 3x = 108 degrees.

If two lines intersect and the measures of the angles formed are in the ratio 2:

Practice Questions

Q1
If two lines intersect and the measures of the angles formed are in the ratio 2:3, what is the measure of the larger angle?
  1. 72 degrees
  2. 108 degrees
  3. 60 degrees
  4. 90 degrees

Questions & Step-by-Step Solutions

If two lines intersect and the measures of the angles formed are in the ratio 2:3, what is the measure of the larger angle?
  • Step 1: Understand that when two lines intersect, they form two pairs of opposite angles.
  • Step 2: Recognize that the angles formed are in the ratio 2:3. We can represent the smaller angle as 2x and the larger angle as 3x.
  • Step 3: Since these two angles are supplementary (they add up to 180 degrees), we can write the equation: 2x + 3x = 180.
  • Step 4: Combine the terms on the left side of the equation: 5x = 180.
  • Step 5: Solve for x by dividing both sides of the equation by 5: x = 180 / 5, which gives x = 36 degrees.
  • Step 6: Now, find the measure of the larger angle by substituting x back into the expression for the larger angle: 3x = 3 * 36 degrees.
  • Step 7: Calculate 3 * 36, which equals 108 degrees. Therefore, the measure of the larger angle is 108 degrees.
  • Angle Relationships – Understanding the relationship between angles formed by intersecting lines, specifically supplementary angles.
  • Ratios – Applying ratios to determine the measures of angles based on given relationships.
  • Algebraic Manipulation – Using algebra to solve for unknowns in equations derived from geometric relationships.
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