The calculation of the angles of a triangle are shown by 2x + 15, x + 20 and 3x + 25. Evaluate the measure of the smallest angle within the triangle.
a. 40°
b. 85°
c. 25°
a. The addition of the measures of the angles of a triangle is 180. Using this information, we will write the equation 2x + 15 + x + 20 + 3x + 25 = 180. Simplify the equation; 6x + 60 = 180. Subtract 60 from both sides; 6x = 120. Divide both sides by 6; x = 20. Now substitute 20 for x in each expression to determine the smallest angle. The smallest angle is found using the expression x + 20; 20 + 20 = 40. If you select b, this was the largest angle within the triangle. If you select c, the original equation was incorrectly shown as 2x + 15 + x + 20 + 3x + 25 = 90.