Question:
The angles of a triangle are arranged in ascending order of magnitude. If the difference between two consecutive angles is 10°, find the three angles.
Solution:
Given that,
The difference between two consecutive angles is 10°
Let x, x+10°, x+20° be the consecutive angles that differ by 10°
We know that,
Sum of all angles in a triangle is 180°
x + x + 10° + x + 20° = 180°
3x + 30° = 180°
⇒ 3x = 180° - 30°
⇒ 3x = 150°
⇒ x = 50°
Therefore, the required angles are
x = 50°
x + 10° = 50° + 10° = 60°
x + 20° = 50° + 20° = 70°
As the difference between two consecutive angles is 10°, the three angles are 50°, 60°, 70°.