Question

In a scalene triangle the first angle is 3 times as large as the second, while the third angle is 20 degrees smaller than the second. Find the size of each angle; hence, name the triangle according to its angles' sizes.

Answer 1

20°, 40°, 120°

Explanation:

The sum of the 3 angles in a triangle = 180°

let the second angle be x then the first angle = 3x ( 3 times the second) and

the third angle = x - 20 ( 20 smaller than the second ), hence

x + 3x + x - 20 = 180

5x - 20 = 180 ( add 20 to both sides )

5x = 200 ( divide both sides by 5 )

x = 40

first angle = 3x = 3 × 40 = 120°

second angle = x = 40° and third angle = x - 20 = 40 - 20 = 20°