Two angles that add to 90° are complementary. If one is 35°, the other is 55°.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Adding to 180
Two angles that add to 180° are supplementary. Angles on a straight line are supplementary.
Vertical angles
Where two lines cross, the angles opposite each other are equal.
Why they must be equal
Each shares a straight line with the same neighbour, so each is 180° minus that neighbour.
Adjacent angles on a line
Angles sitting side by side on a straight line add to 180°, because together they make a straight angle. This is the most frequently used angle fact in all of geometry, and it needs no diagram to remember.
Angles around a point
Angles meeting at a point and filling the whole turn add to 360°. This gives you a second total to work from, and it is why the slices of a pie chart must account for exactly one full turn.
The angles of a triangle
The three angles of any triangle add to 180°. Tear the corners off a paper triangle and place them together and they form a straight line every time. That demonstration is worth doing once — it is more convincing than being told.
Chaining the facts together
Most angle problems need two or three of these facts in sequence: find one angle from a straight line, use it in a triangle, then use that result somewhere else. Write each result on the diagram as you go.
Step 2: Try It Yourself
Set one angle and read what its partner must be.
35° is an acute angle.
Step 3: Watch an Example
One step at a time.
Watch Ana Find Three Angles
Two lines cross, making an angle of 40°.
- Step 1
The angle opposite it is vertical to it, so it is also 40°.
Step 4: Your Turn
Practice makes it stick.
The Complement
Problem 1 of 2
An angle is 25°. What is its complement, in degrees?
The Supplement
Problem 2 of 2
An angle is 110°. What is its supplement, in degrees?
Find the Partner
1 of 4
Complement of 40°?
2 of 4
Supplement of 65°?
3 of 4
Two lines cross at 55°. What is the vertical angle?
4 of 4
That same crossing. What is the angle next to the 55°?
Step 5: Quick Check
Show what you know.
Question 1 of 1
Supplement of 130°?
What You Learned
- Complementary angles add to 90°; supplementary angles add to 180°.
- Angles on a straight line are supplementary.
- Where two lines cross, opposite angles are equal.