Solve problems involving the angles of a triangle
An important result of Euclidean geometry (the geometry of the Greek mathematician Euclid) is that the sum of the angle measures of any triangle is 180°.
Example
Step 1:- Read the problem. We are asked to find the measure of each angle.
Step 2:- Assign a variable. Let x represent the measure of one angle.
Step 3:- Write an equation. The sum of the three measures shown in the figure must be 180°.
x + (x + 20°) + (210° – 3x) = 180°
Step 4:- Solve
-x + 230° = 180°
-x = -50°
x = 50°
Step 5:- State the answer. One angle measure 50°, another measure x + 20° = 50° + 20° = 70°, and third measures 210° – 3x = 210° – 3(50°) = 60°.
Step 6:- Check. Since 50° + 70° + 60° = 180° , the answer is correct.