Angle Relationships — Challenge
Parallel lines cut by a transversal make only two different angles. Knowing which is which unlocks every diagram.
What these problems 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 angles are complementary and one of them is 35 degrees. How many degrees is the other?
- 45
- 55
- 65
- 145
- 325
Worked answer
55
Complementary angles add to 90 degrees.
90-35 = 55 degrees.
Angles adding to 180 would be supplementary, which would give 145.
Problem 2
Two angles are supplementary and one of them is 110 degrees. How many degrees is the other?
- 50
- 60
- 70
- 80
- 250
Worked answer
70
Supplementary angles add to 180 degrees.
180-110 = 70 degrees.
Problem 3
Two angles sit side by side on a straight line. One is 40 degrees. How many degrees is the other?
- 50
- 140
- 320
- 40
- 100
Worked answer
140
Angles on a straight line add to 180 degrees.
180-40 = 140 degrees.
Using 90 instead would give 50, which applies to a right angle rather than a straight line.
Problem 4
Two lines cross. One of the angles formed is 65 degrees. How many degrees is the angle vertically opposite it?
- 25
- 35
- 115
- 65
- 130
Worked answer
65
When two lines cross, the angles directly opposite each other are equal.
So the vertically opposite angle is also 65 degrees.
The angle next to it along a line would be 115 degrees, which is the common confusion.
Problem 5
Two angles of a triangle are 50 and 60 degrees. How many degrees is the third?
- 70
- 60
- 80
- 110
- 170
Worked answer
70
The three angles of a triangle add to 180 degrees.
180-50-60 = 70 degrees.
Adding the two given angles gives 110, which is what remains to be subtracted, not the answer.
Problem 6
A transversal crosses two parallel lines. One co-interior angle is 75 degrees. How many degrees is the other co-interior angle?
- 15
- 75
- 105
- 180
- 285
Worked answer
105
Co-interior angles lie on the same side of the transversal between the parallel lines, and they add to 180 degrees.
180-75 = 105 degrees.
Alternate angles would be equal at 75 degrees, which is a different pair.