Two angles on a straight line add to 180 degrees. They are supplementary.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Complementary
Two angles making a right angle add to 90 degrees.
Vertical angles
When two lines cross, the angles opposite each other are equal.
Turn it into an equation
If one of a supplementary pair is x and the other is 50, then x + 50 = 180.
Complementary and supplementary
Two angles are complementary if they add to 90° and supplementary if they add to 180°. The names are worth learning because they appear constantly, and the totals give you an equation whenever one angle is unknown.
Vertical angles are equal
When two lines cross, the angles opposite each other are equal. This follows from both being supplementary to the same neighbouring angle. It is a small deduction, and it is the kind of reasoning geometry is built from.
Turning the relationship into an equation
If two supplementary angles are x and 3x, then x + 3x = 180, so x = 45. Angle relationships give the total and algebra finds the parts. This is where the equation-solving chapter starts paying off in geometry.
Mark the diagram as you go
Write each angle you work out onto the figure. In a diagram with several crossing lines, an unmarked angle you calculated three steps ago is one you will recalculate or misuse. Marking is how geometric working stays followable.
Step 2: Try It Yourself
Tap and try it out.
The two angles together measure 180°. Angle measures add.
Step 3: Watch an Example
One step at a time.
Watch Ana Find a Missing Angle
Two angles on a straight line, one measuring 65 degrees.
- Step 1
She knows a straight line is 180 degrees.
Step 4: Your Turn
Practice makes it stick.
The Straight Line
Problem 1 of 3
Two supplementary angles, one is 72. What is the other?
degrees
The Right Angle
Problem 2 of 3
Two complementary angles, one is 35. What is the other?
degrees
The Crossing
Problem 3 of 3
Two lines cross. One angle is 40. What is the angle opposite it?
degrees
Find the Angle
1 of 4
Supplementary to 90?
2 of 4
Complementary to 20?
3 of 4
Supplementary to 125?
4 of 4
Two lines cross and one angle is 63. What is the vertical angle?
Step 5: Quick Check
Show what you know.
Question 1 of 2
Supplementary to 47?
Question 2 of 2
What do vertical angles do?
What You Learned
- Supplementary angles add to 180, complementary to 90.
- Vertical angles are equal.
- Write an equation and solve it.