If the angles of a triangle are in the ratio 5:3:7, then the triangle is
(a) an acute angled triangle
(b) an obtuse angled triangle
(c) a right angled triangle
(d) an isosceles triangle
(a) Given, the ratio of angles of a triangle is 5 : 3 : 7.
Let angles of a triangle be ∠A,∠B and ∠C.
Then, ∠A = 5x, ∠B = 3x and ∠C = 7x
In ΔABC, ∠A + ∠B + ∠C = 180° [since, sum of all angles of a triangle is 180°]
5x + 3x + 7x = 180°
=> 15x = 180°
x = 180°/15= 12°
∠A = 5x = 5 x 12° = 60°
∠B = 3x= 3 x 12°= 36°
and ∠C =7x = 7 x 12° = 84°
Since, all angles are less than 90°, hence the triangle is an acute angled triangle.