Two angles that share an arm make one bigger angle. Their measures add.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
An example
A 30 degree turn followed by a 45 degree turn is a 75 degree turn in all.
Finding a missing angle
If the whole is 90 and one part is 35, the other part is 90 − 35.
Why it works
Turning, then turning again, is one longer turn. Nothing is lost between them.
Adjacent angles add
Two angles that share a vertex and an arm, sitting side by side, combine into one larger angle whose measure is the sum. Turning 30° and then 40° more is the same as turning 70° in one go. Angles add because turns add.
Finding a missing angle
If two angles make a right angle and one is 35°, the other is 90 - 35 = 55°. If they make a straight angle and one is 110°, the other is 70°. These are missing-addend problems with the total supplied by geometry.
Angles around a point
Several angles meeting at a point and filling the whole turn must add to 360°. That gives you another total to work from, and it is why a pie chart's slices always account for exactly one full turn.
Check the answer against the picture
If you calculate a missing angle as 140° but it is drawn clearly smaller than a right angle, something is wrong. Diagrams are rarely to scale but they are usually roughly right, and a wildly mismatched answer deserves a second look.
Step 2: Try It Yourself
Two angles sharing an arm. The total is written below.
The two angles together measure 75°. Angle measures add.
Step 3: Watch an Example
One step at a time.
Watch Ana Find a Missing Angle
A right angle is split into two parts. One is 35 degrees.
- Step 1
She knows the whole right angle is 90 degrees.
Step 4: Your Turn
Practice makes it stick.
Two Turns
Problem 1 of 2
A 40 degree turn and then a 25 degree turn. How many degrees in all?
degrees
The Missing Part
Problem 2 of 2
A straight angle is split into 110 degrees and one more part. How big is that part?
degrees
Add and Subtract Turns
1 of 4
35 degrees plus 55 degrees?
2 of 4
A right angle split into 20 and one more part. How big is that part?
3 of 4
A straight angle split into 65 and one more part. How big is that part?
4 of 4
90 degrees plus 90 degrees?
Step 5: Quick Check
Show what you know.
Question 1 of 2
A right angle split into 25 and one more part. How big is that part?
Question 2 of 2
What happens to angle measures when two angles sit side by side?
What You Learned
- Angles sharing an arm add together.
- A missing part is found by subtracting.
- Turning twice is one longer turn.