4.04 Triangles and Angles

Interior Angles

Sum of Interior Angles of a Triangle

m∠A + m∠B = m∠C = ____°

Why? Because the angle measurements form a straight line and the measurement of a straight angle is 180°. Complete this Geogebra activity to see if the sum changes if you change the shape of the triangle.

A triangle with three angles: angle A is 92.26 degrees, angle B is 56.85 degrees, and angle C is 30.89 degrees

Triangle Sum Theorem

m∠A + m∠B = m∠C = 180°

Given any ∠ABC, the sum of the interior angles = 180°.

A triangle with three angles: angle A is 72.84 degrees, angle B is 55.76 degrees, and angle C is 51.4 degrees

This is one of the most useful theorems in GEOMETRY! To find the valus of x, we just write an equation. Since all three angles must add to equal 180°, we can make an equation.

x + 24° + 119° = 180°

Then solve.

A triangle with three angles: The first angle is 119 degrees, the second angle is 24 degrees, and the third angle is of value x degrees

Add like terms on the left side.

x + 24° + 119° = 180°

x + 143° = 180°

Subtract 143° on both sides

x = 37°

You just found the value of x! Watch this video for more information.

Your Turn

Find the value of x.

Since all three angles must add to equal 180°, you have enough information to solve for x.

A triangle with three angles: The first angle is 89 degrees, the second angle is 56 degrees, and the third angle is of value x degrees

Write the equation.

x + 56° + 89° = ___°

Add like terms. x + ___° = 180°

x + ___

Watch this video for more information.

Algebraic Expressions

Sometimes the angles are written as algebraic expressions with more than one term. You would still write the equation = 180° then solve.

(x + 10) + 56° + 89° = 180°

x + 10 + 56° + 89° = 180°

A triangle with three angles: The first angle is 89 degrees, the second angle is 56 degrees, and the third angle is of value x+10 degrees