Triangle Angle Sum

Properties of triangles

Triangles have three sides and three angles

Triangles are named according to their vertices

The sum of the angle measurements of a triangle is 180°

Examples

Since all of the angles must add up to 180° and two of the angles add up to 100 (50+50), then the third angle must be 80°

More Examples

Since the two known angles add up to 78° (44 + 34), the third angle is 102° (180 – 78).

Using Algebra to Find The Missing Angle Measurement

To find the measurement of angle A, we must set up an equation and then solve:

53 + x + x + 59 + 82 = 180 2x + 194 = 180 -194 -194 2x = -14 2 2 x = -7Now, substitute x with -7 in the

expression to find the measurement of angle A:

53 + x = 53 + -7 = 46°

Another Example

Solution to find the measurement of angle A:

6x – 1 + 8x + 7 + 90 = 180 14x + 96 = 180 - 96 - 96 14x = 84 14 14 x = 66x –1 = 6(6) – 1 = 36 – 1 = 35So, angle A is 35°

For You To Try

Find the measurement of angle A.

Solution:3x + 2 + 5x + 130 = 180 8x + 132 = 180 - 132 -132 8x = 48 8 8 x = 63x + 2 = 3(6) + 2 = 18 + 2 = 20 So, the measurement of angle A

is 20°

ExtensionTo find the measurement of the

missing angle, we must use what we know about angles and triangles:1. The measurement of the missing angle of the triangle on the left must be 53° according to the properties of triangles.

2. Because straight angles are 180° and the angles that form a straight angle must add up to 180, then the measurement of the left-side angle of the triangle on the right must be 44° (180 – 83 – 53).

3. So, according to the properties of triangles, the unknown angle measurement is 50° (180 – 86 – 44)

For You To TryFind the unknown angle

measurement.Solution:1. According to the properties of

triangles, the missing angle measurement of the triangle on the left is 54° (180 – 85 – 41)

2. The angle measurement of the angle on the left of the triangle on the right is also 54° because of the properties of vertical angles

3. So, according to the properties of triangles, the unknown angle measurement is 64°