What are vertical angles?

Pairs of angles formed directly across from each other when two lines intersect. They are always equal.

Why called "vertical" if not pointing up?

From Latin vertex (point), referring to the shared intersection point, not the direction.

Can vertical angles be right angles?

Yes. When lines are perpendicular, all four angles are 90°.

Vertical Angles Worksheet

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Vertical Angles Worksheet

Name:Date:Class:

1.Two lines intersect forming an angle of

122°

. Find the vertical angle.

2.Two lines intersect forming an angle of

149°

. Find the vertical angle.

3.Two lines intersect forming an angle of

119°

. Find the vertical angle.

4.Two lines intersect forming an angle of

54°

. Find the vertical angle.

5.Two lines intersect forming an angle of

46°

. Find the vertical angle.

6.Two lines intersect forming an angle of

40°

. Find the vertical angle.

7.Two lines intersect forming an angle of

63°

. Find the vertical angle.

8.Two lines intersect forming an angle of

23°

. Find the vertical angle.

9.Two lines intersect forming an angle of

44°

. Find the vertical angle.

10.Two lines intersect forming an angle of

109°

. Find the vertical angle.

11.Two lines intersect forming an angle of

112°

. Find the vertical angle.

12.Two lines intersect forming an angle of

137°

. Find the vertical angle.

13.Two lines intersect forming an angle of

133°

. Find the vertical angle.

14.Two lines intersect forming an angle of

144°

. Find the vertical angle.

15.Two lines intersect forming an angle of

149°

. Find the vertical angle.

16.Two lines intersect forming an angle of

104°

. Find the vertical angle.

17.Two lines intersect forming an angle of

10°

. Find the vertical angle.

18.Two lines intersect forming an angle of

112°

. Find the vertical angle.

19.Two lines intersect forming an angle of

55°

. Find the vertical angle.

20.Two lines intersect forming an angle of

80°

. Find the vertical angle.

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Worked Example

Problem: Two lines intersect. One angle is (3x + 15)° and its vertical angle is (5x − 9)°. Find x.

3x + 15 = 5x − 9— Vertical angles are equal.
15 + 9 = 5x − 3x, so 24 = 2x— Collect terms.
x = 12, angle = 3(12) + 15 = 51°— Solve and substitute.

Answer: x = 12, both angles = 51°

Vertical Angles Worksheet

Vertical Angles Worksheet

Answer Key

Worked Example

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