Triangle angle sum worksheet

Grade 8 math, Common Core 8.G.A.5. 10 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

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Triangle angle sum

Grade 8 math, Common Core 8.G.A.5

Find each missing angle or the value of x.

1.
Two angles of a triangle measure 24° and 113°. Find the third angle.
2.
The angles of a triangle measure x°, 2x° and 6x°. Find x and each angle.
3.
A right triangle has one angle of 57°. Find the other two angles.
4.
Two angles of a triangle measure 22° and 77°. Find the third angle.
5.
A right triangle has one angle of 65°. Find the other two angles.
6.
The angles of a triangle measure x°, 4x° and 4x°. Find x and each angle.
7.
Two interior angles of a triangle measure 45° and 80°. What is the exterior angle at the third corner?
8.
Two angles of a triangle measure 63° and 43°. Find the third angle.
9.
Two angles of a triangle measure 31° and 70°. Find the third angle.
10.
Two angles of a triangle measure 93° and 27°. Find the third angle.

Answer key: Triangle angle sum

Grade 8 math. Each answer has a few worked steps, to help check the method as well as the answer.

1. 43°
180 − 24 − 113 = 43
2. x = 20; 20°, 40° and 120°
9x = 180x = 20
3. 90° and 33°
90 − 57 = 33
4. 81°
180 − 22 − 77 = 81
5. 90° and 25°
90 − 65 = 25
6. x = 20; 20°, 80° and 80°
9x = 180x = 20
7. 125°
The exterior angle equals the sum of the two far-away interior angles45 + 80 = 125
8. 74°
180 − 63 − 43 = 74
9. 79°
180 − 31 − 70 = 79
10. 60°
180 − 93 − 27 = 60

The answer key prints on its own page. You’re welcome to print and copy these worksheets for your own kids or class.

About triangle angle sum

The three angles of any triangle add up to 180°. An exterior angle (made by extending one side) equals the sum of the two interior angles that aren’t next to it. In an isosceles triangle, the two base angles are equal.

Worked example 1

A right triangle has one angle of 49°. Find the other two angles.

Step 1.90 − 49 = 41

Answer: 90° and 41°

Worked example 2

Two angles of a triangle measure 67° and 56°. Find the third angle.

Step 1.180 − 67 − 56 = 57

Answer: 57°

Worked example 3

An isosceles triangle has a top (vertex) angle of 106°. Find each base angle.

Step 1.(180 − 106) ÷ 2 = 37

Answer: 37°

Watch out for

Add the angles you know and subtract from 180°.
An exterior angle equals the sum of the two far-away interior angles.
In a right triangle, the two smaller angles add up to 90°.

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