HSPT: Geometry: find a missing triangle angle
Learn to find a missing angle in any triangle, including right and isosceles triangles, using the 180° total.
How do you find the third angle of a triangle when you know the other two?
Short answer
The three inside angles of a triangle always add to 180°. Subtract the angles you know from 180° to find the missing one.
Know first: Measuring angles in degrees, Right angles
Step 1 of 5
The three angles of a triangle add to 180°
In every triangle, the three inside angles add up to 180°. It doesn't matter how big the triangle is or what shape it has.
So if you know two angles, subtract both from 180° to get the third. Some triangles give you one angle for free: a right angle is 90°, and the two base angles of an isosceles triangle are equal.
| Triangle | What you know | How to find a missing angle |
|---|---|---|
| Any triangle | Angles total 180° | 180 − the two known angles |
| Right triangle | One angle is 90° | The other two total 90° |
| Isosceles triangle | Two angles are equal | Subtract the unequal angle from 180, then halve |
Step 2 of 5
Subtract the known angles from 180°
Worked example: Two angles known
Two angles of a triangle measure 52° and 74°. What is the third angle?
- A54°
- B126°
- C306°
- D38°
- 1
Add the known angles
52 + 74 = 126.
- 2
Subtract from 180
180 − 126 = 54.
- 3
Check
52 + 74 + 54 = 180.
- 4
See why the other choices are there
126 is the sum of the two known angles, not the missing one. 306 adds 180 instead of subtracting from it. 38 subtracts 52 from 90, as if this were a right triangle.
Answer
54°
Wrong: 360 − 52 − 74 = 234°
Right: 180 − 52 − 74 = 54°
360° is the total for a four-sided shape or a full turn. A triangle's angles total 180°, and no triangle angle can be 180° or more.
Step 3 of 5
Use the 180° total
Check yourself · Question 1
In a right triangle, one of the acute angles measures 27°. What is the other acute angle?
Answer: C
The right angle is 90°, so the other two angles total 180 − 90 = 90°. The missing angle is 90 − 27 = 63°.
Check yourself · Question 2
An isosceles triangle has a top angle of 40°. Its two base angles are equal. What is each base angle?
Answer: B
The base angles share 180 − 40 = 140°. Split it evenly: 140 ÷ 2 = 70°. Check: 70 + 70 + 40 = 180.
Trap answer: 140°
Forgetting to split
- Why it looks right
- 180 − 40 is the natural first step, and the result looks like a finished answer.
- Why it's wrong
- 140° is shared by two equal base angles. One angle alone is half of that.
- The right answer
- 70°, because 70 + 70 + 40 = 180.
Common mistake
"I subtract the angles I know from 360."
- Why it's tempting
- 360° shows up for full circles and four-sided shapes, so the number is familiar.
- Do this instead
- Triangles total 180°. A quick check: every angle in a triangle must be less than 180°.
Step 4 of 5
What to remember
Remember
- The inside angles of any triangle add to 180°.
- In a right triangle, the other two angles total 90°.
- In an isosceles triangle, subtract the odd angle from 180° and split the rest evenly.
Step 5 of 5
Practice on a real question
Use what you just learned on this question, then check the explanation.
In your own words
What did the two given angles add up to in the practice question, and which wrong choice is that sum?