1.

The angles of a triangle are (x + 10)°, (x – 20)° and (x + 40)°. Find the value of x and the measure of the angles.

Answer»

Given that the angles of the triangle are 

(x + 10)°, (x – 20)° and (x + 40)° 

(x + 10)° + (x – 20)° + (x + 40)° = 180°

⇒ x + 10° + x – 20° + x + 40° = 180° 

⇒ 3x + 30° = 180° 

⇒ 3x – 180° – 30° 

⇒ 3x = 150°

⇒ x = 150°/3 = 50°

The angles are, 

x + 10° = 50° + 10° = 60° 

x – 20° = 50° – 20° = 30° 

x + 40° = 50° + 40° = 90° 

∴ Measure of the angles are 60°, 30° and 90°.



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