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.
(Class 10 Maths Sample Question Paper)
(Class 10 Maths Sample Question Paper)
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Solution: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° -d
d+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°.
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