The measures of the angles of a triangle are in the ratio of 3:4:5. Evaluate of the largest angle.
a. 75°
b. 37.5°
c. 45°
d. 60°
a. The addition of the measures of the angles of a triangle is 180°. Using this fact we can establish the following equation: 3x + 4x + 5x = 180. Simplifying; 12x = 180. Split both sides by 12; x = 15. The largest angle is shown by 5x. Thus, 5x, or 5(15), equals 75, the measure of the largest angle. If you select b, the original equation was set equal to 90 rather than 180. If you select c, this was the smallest angle within the triangle. If you select d, this was the angle whose measurement lies between the largest and smallest angles.