**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.