Angle Relationships — Drills
Angle Relationships has 7 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills 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.
Parallel lines
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Two parallel lines are cut by a transversal. One angle is 93°. Find its alternate interior angle.
Worked answer
93
Alternate interior angles are equal.
93°
Problem 2
Two parallel lines are cut by a transversal. One angle is 124°. Find its alternate interior angle.
Worked answer
124
Alternate interior angles are equal.
124°
Triangle
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A triangle has angles 67° and 64°. Find the third.
Worked answer
49
67 + 64 = 131
180 - 131 = 49
Problem 2
A triangle has angles 88° and 43°. Find the third.
Worked answer
49
88 + 43 = 131
180 - 131 = 49
Vertical
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Two lines cross. One angle is 93°. Find the angle next to it.
Worked answer
87
180 - 93 = 87
87°
Problem 2
Two lines cross. One angle is 129°. Find the angle vertically opposite it.
Worked answer
129
Vertical angles are always equal, parallel lines or not.
129°
Exterior
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A triangle has interior angles 54° and 56°. Find the exterior angle at the third vertex.
Worked answer
110
54 + 56 = 110
Check: third angle is 70, and 180 - 70 = 110 ✓
Problem 2
A triangle has interior angles 67° and 47°. Find the exterior angle at the third vertex.
Worked answer
114
67 + 47 = 114
Check: third angle is 66, and 180 - 66 = 114 ✓
Solving
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Two parallel lines are cut by a transversal. Corresponding angles measure (5x + 7)° and (9x - 73)°. Find x.
Worked answer
20
5x + 7 = 9x - 73
80 = 4x
x = 20
Both angles are 107° ✓
Problem 2
Two parallel lines are cut by a transversal. Corresponding angles measure (4x + 35)° and (7x - 40)°. Find x.
Worked answer
25
4x + 35 = 7x - 40
75 = 3x
x = 25
Both angles are 135° ✓
Aa
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Triangle 1 has angles 58° and 75°. Triangle 2 has angles 58° and 76°. Are they similar? Answer yes or no.
Worked answer
no
Triangle 1: 58, 75, 47
Triangle 2: 58, 76, 46
Different angle sets, so not similar.
Problem 2
Triangle 1 has angles 70° and 58°. Triangle 2 has angles 70° and 58°. Are they similar? Answer yes or no.
Worked answer
yes
Triangle 1: 70, 58, 52
Triangle 2: 70, 58, 52
The same three angles, so similar by AA.
Polygon
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the sum of the interior angles of a hendecagon.
Worked answer
1620
n = 11, so 11 - 2 = 9 triangles
9 × 180 = 1620
Problem 2
Find the sum of the interior angles of a triangle.
Worked answer
180
n = 3, so 3 - 2 = 1 triangles
1 × 180 = 180