Question

If the angles of a triangle are in ratio of 1:2:3, find the sizes of angles .What is the sum of largest and smallest angles​

Answer 1

Sum of the Largest Angle = 150°
Sum of the Smallest Angle = 90°

Let x be the measure of angle
Angle 1 = x
Angle 2 = 2x
Angle 3 = 3x
Sum of all angle in a triangle= 180°
So, x + 2x + 3x = 180°
6x = 180°
x = 30°
So,
Angle 1 = 30°
Angle 2= 2x = 2*30 = 60°
Angle 3 = 3x = 3*30 = 90°

Answer 2

see explanation

Explanation:

sum the parts of the ratio, 1 + 2 + 3 = 6 parts

divide the sum of the angles in a triangle , 180° by 6 to find the value of one part of the ratio.

180° ÷ 6 = 30° ← value of 1 part of the ratio , the smallest , then

2 parts = 2 × 30° = 60°

3 parts = 3 × 30° = 90° , the largest angle

the angle sizes are 30° , 60° , 90°

smallest + largest = 30° + 90° = 120°