opposite angles


Definition of Opposite Angles

  • When two lines intersect, four angles are formed. The angles that are directly opposite to each other are called Opposite Angles.

More about Opposite Angles

  • Opposite angles are also called vertically opposite angles.
  • Opposite angles are always non-adjacent.
  • When two parallel lines are cut by a transversal, 8 angles or 4 pairs of opposite angles are formed.

Example of Opposite Angles

  • In the given figure, the lines l and p intersect each other and form four angles. Among these angles, ∠1 and ∠3, ∠2 and ∠4 are opposite angles.

Solved Example on Opposite Angles

Find the pairs of opposite angles in the given figure.

Choices:
A. (a, b), (c, d), (e, f), (g, h)
B. (a, e), (b, f), (c, g), (d, h)
C. (a, c), (b, d), (e, g), (f, h)
D. (a, d), (b, c), (e, h), (f, g)
Correct Answer: C
Solution:
Step 1: When two lines intersect, four angles are formed. The angles that are directly opposite to each other are called opposite angles.
Step 2: From the figure, two lines PQ and RS are cut by the transversal TU forming eight angles.
Step 3: So, (a, c), (b, d), (e, g), (f, h) are opposite angles.

Related Terms for Opposite Angles

  • Adjacent Angles
  • Intersect
  • Line
  • Transversal