19. The angles of a triangle are in AP. If the greatest angle equals t

1.	19. The angles of a triangle are in AP. If the greatest angle equals to the sum of the other two.then find the angles. Also, find these angles are multiple of which angle.
Answer» Let the three angles of a triangle are (a-d),(a),& (a+d).(a-d)+(a)+ (a+d) = 180°3a = 180°a= 180 /3 = 60 ° The 3 angles are 60° -d , 60° and 60°+ d. ATQ Greatest angle = sum of two smaller angles 60° + d = 60° -d + 60°60° + d = 120° -dd+d = 120° -60°2d = 60°d = 60° /2= 30°d = 30° Required angles of a triangle are (60° -30°) , (60°) and (60° + 30°)= 30° , 60°, 90°. Hence, the required angles of a triangle are 30° , 60°, 90°. These angles are the multiple of 30°.

19. The angles of a triangle are in AP. If the greatest angle equals to the sum of the other two.then find the angles. Also, find these angles are multiple of which angle.

Answer»

Let the three angles of a triangle are (a-d),(a),& (a+d).(a-d)+(a)+ (a+d) = 180°3a = 180°a= 180 /3 = 60 ° The 3 angles are 60° -d , 60° and 60°+ d.

ATQ

Greatest angle = sum of two smaller angles

60° + d = 60° -d + 60°60° + d = 120° -dd+d = 120° -60°2d = 60°d = 60° /2= 30°d = 30°

Required angles of a triangle are (60° -30°) , (60°) and (60° + 30°)= 30° , 60°, 90°.

Hence, the required angles of a triangle are 30° , 60°, 90°.

These angles are the multiple of 30°.