Geometry Angle Theorems

Question 1

What are vertical angles?

Answer 1

They are congruent and are opposite to each other in the corners of the “X” shape created by the intersecting lines.

Question 2

What are corresponding angles?

Answer 2

They are on the same side of the transversal, with one angle being interior and the other exterior. When the two intersected lines are parallel, corresponding angles are always congruent, meaning they have equal measures.

Question 3

What are alternate interior angles?

Answer 3

Angles inside the lines, on opposite sides of the transversal; equal if lines are parallel.

Question 4

What are alternate exterior angles

Answer 4

Angles outside the lines, on opposite sides of the transversal; equal if lines are parallel.

Question 5

What are consecutive interior angles?

Answer 5

Angles inside the lines, on the same side of the transversal; they add up to 180° if lines are parallel.

Question 6

If one angle is (8x – 9)° and the other is 99°, and they’re alternate exterior angles, what is x?

Answer 6

8x – 9 = 99 → x = 13.5

Question 7

If one angle is (19x + 11)° and the other is 55°, and they’re consecutive interior angles, what is x?

Answer 7

They add to 180 → x = 6.

Question 8

If one angle is (14x – 2)° and the other is (12x + 14)°, and they’re alternate exterior angles, what is x?

Answer 8

Set them equal → x = 8.

Question 9

If one angle is (5x + 1)° and the other is (4x + 12)°, and they’re corresponding, what is x?

Answer 9

Set them equal → x = 11.

Question 10

If one angle is (14x – 4)° and the other is (15x + 10)°, and they’re consecutive interior, what is x?

Answer 10

Add them to 180 → x = 6.

Question 11

If corresponding angles are equal, what does that mean about the lines?

Answer 11

The lines are parallel.

Question 12

If alternate interior angles are equal, what does that mean about the lines?

Answer 12

The lines are parallel.

Question 13

If consecutive interior angles add to 180, what does that mean about the lines?

Answer 13

The lines are parallel.

Question 14

If (2x + 15)° and 135° are corresponding angles, what is x?

Answer 14

Set equal → x = 60.

Question 15

If (3x – 15)° and 150° are consecutive interior angles, what is x?

Answer 15

Add to 180 → x = 15.

Question 16

If (x + 2)° and 58° are alternate interior angles, what is x?

Answer 16

Set equal → x = 56

Question 17

What are supplementary angles?

Answer 17

Two angles that add up to 180°.

Question 18

What are vertical angles?

Answer 18

Opposite angles when lines cross; they’re equal.

Question 19

What’s the Transitive Property?

Answer 19

If A = B and B = C, then A = C.

Question 20

What is the Consecutive Interior Angles Converse?

Answer 20

If two inside same-side angles add to 180, the lines are parallel.