Across the crossing
Angles that face each other at a crossing are equal.
Across from 120°
Two lines cross. ∠a = 120° and ∠b = 60°. The angle ∠c is across the crossing from ∠a.
How big is ∠c?
What this lesson covers
The idea
Opposite angles formed by two intersecting lines are called vertically opposite angles, and they are always equal, since each forms a linear pair with the same angle.
Across from 120°
Two lines cross. ∠a = 120° and ∠b = 60°. The angle ∠c is across the crossing from ∠a.
How big is ∠c?
- 60°
- 120°
- 180°
Two bars, one gap
Keep one angle. The two angles next to it each finish a straight bar. Compare the two bars.
Opposite angles are equal
Look at ∠a and ∠c. Each makes a linear pair with ∠b. So ∠a + ∠b = 180° and ∠c + ∠b = 180°.
Both angles fill what ∠b leaves of 180°. The same space gives the same size, so ∠a = ∠c. In the same way ∠b = ∠d.
Opposite angles formed by two intersecting lines are called vertically opposite angles. They are always equal, since each forms a linear pair with the same angle.
- Across from each other | Equal because
- ∠a and ∠c | both make 180° with ∠b
- ∠b and ∠d | both make 180° with ∠a
Notes
Opposite angles formed by two intersecting lines are called vertically opposite angles. They are always equal, since each forms a linear pair with the same angle.
Check yourself
Two lines cross. ∠a = 47°. ∠c is the angle across from ∠a. Find ∠a + ∠c.
Answer: 94 °
∠a and ∠c are vertically opposite, so ∠c = ∠a = 47°. Then ∠a + ∠c = 47° + 47° = 94°.
Which angle is vertically opposite to the shaded angle ∠b?
Two lines cross. ∠c = 70°. Find ∠b.
Answer: 110 °
∠b is next to ∠c, so ∠b + ∠c = 180° and ∠b = 180° − 70° = 110°.
Why do we call them vertically opposite angles?
- ∠d — correct. Yes! ∠d is across the crossing from ∠b.
- ∠a. ∠a is next to ∠b. They form a linear pair, and they add up to 180°.
- ∠c. ∠c is next to ∠b. They form a linear pair, and they add up to 180°.
- One of them is above the other.. It has nothing to do with up and down. Turn the page and the angles across the crossing are still vertically opposite.
- The two lines must stand upright.. The lines can lie in any direction. Any two crossing lines make vertically opposite angles.
- They are opposite each other at the crossing point, the vertex. — correct. Yes! The word is about the vertex, the point where the lines cross.