Missing Angles: Step-by-Step Guide
In many shapes, the angles add up to a number you can count on. The angles in a triangle add up to 180 degrees. The angles in a four-sided shape add up to 360 degrees. Angles on a straight line add up to 180 degrees, and angles all the way around a point add up to 360 degrees. To find a missing angle, add up the angles you know and subtract that from the total.
Math Racer skill guide · Middle School · Grades 6-8
How to solve it, step by step
- Decide what kind of figure it is. Is it a triangle, a four-sided shape, a straight line, or angles around a point? This tells you what total to use.\[\triangle: 180^\circ,\;\square: 360^\circ,\;\text{line}: 180^\circ,\;\text{point}: 360^\circ\]
- Write an equation. Add the angles you know, plus x for the missing angle, and set it equal to the total.\[a + b + x = 180^\circ\]
- Solve for the missing angle. Subtract the known angles from the total to get x.\[x = 180^\circ - a - b\]
- Check that it makes sense. Your angle should be positive, and all the angles together should add up to the total.\[0^\circ < x < 180^\circ\]
Worked example
A triangle has two angles measuring 47 degrees and 68 degrees. Find the third angle.
Step 1: It is a triangle, so the three angles add up to 180 degrees.
Step 2: Write the equation: 47 + 68 + x = 180.
Step 3: Add the known angles: 47 + 68 = 115.
Step 4: Subtract: x = 180 - 115 = 65 degrees.
Step 5: Check: 47 + 68 + 65 = 180. Correct.
The missing angle is 65 degrees.
Tips and common mistakes
- Remember these totals: triangle = 180, four-sided shape = 360, straight line = 180, full circle = 360.
- For a shape with n sides, the inside angles add up to (n - 2) x 180 degrees.
- In an isosceles triangle, two of the angles are equal. This can give you extra clues.
- In an equilateral triangle, all three angles are 60 degrees.
- A right triangle has one 90 degree angle, so the other two angles add up to 90 degrees.
- Your answer should always be positive. Add all the angles at the end to check.
- An outside angle of a triangle equals the sum of the two inside angles that are not next to it.