Angle Relationships — Practice
Parallel lines cut by a transversal make only two different angles. Knowing which is which unlocks every diagram.
What these questions cover
These questions use 11 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Vertex — A flat surface; a line where two faces meet; a corner point.
- Supplementary — Two angles summing to 90° / to 180°.
- Vertical angles — The opposite pair formed by two crossing lines — always equal.
- Base — The number being multiplied. In 53 the base is 5.
- Transversal — A line that crosses two or more other lines.
- Corresponding angles — Same position at each crossing. Equal when the lines are parallel.
- Alternate interior angles — Between the parallels, on opposite sides of the transversal. Equal.
- Co-interior angles — Between the parallels, same side. They add to 180°.
- Exterior angle — The angle formed by extending one side of a triangle.
- Parallel — Same slope, different intercept.
- Polygon — A closed figure made of straight segments that meet only at endpoints.
Problem 1
Two parallel lines are cut by a transversal. One angle is 64°. Find its corresponding angle.
Worked answer
64
Same position at the other crossing
64°
Problem 2
Two parallel lines are cut by a transversal. One angle is 110°. Find the co-interior angle on the same side.
Worked answer
70
180 - 110 = 70
70°
Problem 3
An angle of 48° has an alternate interior partner. Find it.
Worked answer
48
The Z shape gives equal angles
48°
Problem 4
A triangle has angles 52° and 71°. Find the third.
Worked answer
57
52 + 71 = 123
180 - 123 = 57
57°
Problem 5
Two lines cross. One angle is 37°. Find the angle vertically opposite it.
Worked answer
37
No parallel lines needed
37°
Problem 6
A triangle has interior angles 38° and 59°. Find the exterior angle at the third vertex.
Worked answer
97
38 + 59 = 97
97°
Problem 7
Two parallel lines are cut by a transversal. Corresponding angles measure (2x + 15)° and (4x - 25)°. Find x.
Worked answer
20
2x + 15 = 4x - 25
40 = 2x
x = 20
Problem 8
Co-interior angles measure (3x)° and (2x + 30)°. Find x.
Worked answer
30
3x + 2x + 30 = 180
5x = 150
x = 30
Problem 9
An isosceles triangle has a vertex angle of 44°. Find each base angle.
Worked answer
68
180 - 44 = 136
136 ÷ 2 = 68
68°
Problem 10
A triangle has angles (x)°, (2x)° and (3x)°. Find the largest angle.
Worked answer
90
6x = 180, so x = 30
Largest is 3x = 90
90°
Problem 11
Which pair of angles is not necessarily equal when two parallel lines are cut by a transversal?
- Co-interior angles
- Corresponding angles
- Alternate interior angles
- Vertical angles
Worked answer
Co-interior angles
Co-interior angles are supplementary, not equal
They are only equal in the special case of 90° each
Problem 12
An exterior angle of a triangle is 128° and one remote interior angle is 55°. Find the other remote interior angle.
Worked answer
73
128 - 55 = 73
73°
Problem 13
Two triangles have angles 40° and 75° in the first, and 75° and 65° in the second. Are they similar? Answer yes or no.
Worked answer
yes
First: 180 - 40 - 75 = 65
Second: 180 - 75 - 65 = 40
Both have 40, 65, 75, so they are similar by AA
Problem 14
Two parallel lines are cut by a transversal. One angle is (5x - 10)° and the co-interior angle is (3x + 6)°. Find both angles.
Worked answer
105 and 75
5x - 10 + 3x + 6 = 180
8x = 184, so x = 23
5(23) - 10 = 105 and 3(23) + 6 = 75
Check: 105 + 75 = 180 ✓
Problem 15
Find the sum of the interior angles of a hexagon.
Worked answer
720
n = 6, so 6 - 2 = 4 triangles
4 × 180 = 720
720°
Problem 16
In a triangle, the second angle is twice the first and the third is 20° more than the first. Find the smallest angle.
Worked answer
40
x + 2x + (x + 20) = 180
4x = 160, so x = 40
Angles are 40, 80, 60; smallest is 40°