The angles of a triangle in ascending order are x, y and z. If y - x = z - y = 10°, then find the angles of the triangle.

Given,

The three angles of the triangle in ascending order are x, y, and z.

Given,

⇒ y − x = 10°

⇒ y = 10° + x     ….(1)

Given,

⇒ z − y = 10°     ….(2)

Substitute value of y from equation (1) in (2), we get :

⇒ z − y = 10°

⇒ z - (10° + x) = 10°

⇒ z = 10° + 10° + x

⇒ z = 20° + x.

So, the three angles of the triangle in terms of x are:

First angle: x

Second angle: x + 10°

Third angle: x + 20°

We know that,

The sum of the angles in any triangle is always 180°.

⇒ x + y + z = 180°

⇒ x + (x + 10°) + (x + 20°) = 180°

⇒ 3x + 30° = 180°

⇒ 3x = 180° − 30°

⇒ 3x = 150°

⇒ x = $\dfrac{150°}{3}$

⇒ x = 50°.

Substituting the value of x,

⇒ y = x + 10° = 50° + 10° = 60°

⇒ z = x + 20° = 50° + 20° = 70°.

Hence, x = 50°, y = 60°, z = 70°.