Answer :

Let us draw a ΔABC.

It is given to us that the angles of the triangle are in the ration 5: 3: 7.

⇒ ∠A:∠B:∠C = 5:3:7

Let us say, ∠A = 5x, ∠B = 3x, and ∠C = 7x - - - - (i)

We know that the sum of the angles of a triangle is equal to 180°.

⇒ ∠A + ∠B + ∠C = 180°

⇒ 5x + 3x + 7x = 180°

⇒ 15x = 180°

⇒ x = (180/15)°

⇒ x = 12° - - - - (ii)

Substituting the value of x = 12° from equation (ii) in equation (i), we get

∠A = 5x = 5 × 12° = 60°,

∠B = 3x = 3 × 12° = 36°,

∠C = 7x = 7 × 12° = 84°

So, we have ∠A = 60°, ∠B = 36°, ∠C = 84°

Since all the three angles of the triangle are less than 90°, it is an acute angled triangle.

So, option (A) is correct.

Option (B) is not correct because an obtuse angled triangle is a triangle with one obtuse angle, i.e., one angle is greater than 90° and other two angles are acute angles, i.e., the two angles are less than 90°. But, here all the three angles are less than 90°. So, it is not an obtuse angled triangle.

Option (C) is not correct, because a right triangle is a triangle with one angle equal to 90°. But, here none of the angles is equal to 90°. Instead, all the angles are less than 90°. So, it is not a right triangle.

Option (D) is not correct, because an isosceles triangle has atleast two equal sides, i.e., two equal angles. But, here all the three angles are different from each other, with no two angles equal to each other. So, it is not an isosceles triangle.

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