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If two lines intersect, what is the sum of the angles formed at the intersection

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Question: If two lines intersect, what is the sum of the angles formed at the intersection? (2021)

Options:

  1. 90 degrees
  2. 180 degrees
  3. 360 degrees
  4. 270 degrees

Correct Answer: 180 degrees

Exam Year: 2021

Solution: 

When two lines intersect, they form two pairs of vertically opposite angles. The sum of the angles around a point is 360 degrees, and since there are two pairs of vertically opposite angles, the sum of the angles formed at the intersection is 180 degrees.

If two lines intersect, what is the sum of the angles formed at the intersection

Practice Questions

Q1
If two lines intersect, what is the sum of the angles formed at the intersection? (2021)
  1. 90 degrees
  2. 180 degrees
  3. 360 degrees
  4. 270 degrees

Questions & Step-by-Step Solutions

If two lines intersect, what is the sum of the angles formed at the intersection? (2021)
  • Step 1: Understand that when two lines intersect, they cross each other at a point.
  • Step 2: Recognize that this intersection creates four angles around that point.
  • Step 3: Identify that these four angles can be grouped into two pairs of vertically opposite angles.
  • Step 4: Know that vertically opposite angles are equal, meaning each pair has the same measure.
  • Step 5: Remember that the total sum of all angles around a point is 360 degrees.
  • Step 6: Since there are two pairs of equal angles, we can say that the sum of the angles in one pair is 180 degrees.
  • Step 7: Conclude that the sum of the angles formed at the intersection of the two lines is 180 degrees.
  • Angle Relationships – Understanding how angles relate to each other when two lines intersect, including vertically opposite angles and the sum of angles around a point.
  • Sum of Angles – Knowledge that the total sum of angles around a point is 360 degrees, and how this applies to intersecting lines.
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