The angles of a triangle are in the ratio 5 : 3 : 7. The triangle is
a) an acute angled triangle
b) an obtuse angled triangle
c) a right triangle
d) an isosceles triangle

Solution:

Given, the angles of a triangle are in the ratio 5 : 3 : 7

We have to find the type of triangle.

We know that the sum of all three interior angles of a triangle is always equal to 180°

Let us consider a triangle ABC

∠A + ∠B + ∠C = 180°

Given, ∠A = 5x

∠B = 3x

∠C = 7x

So, 5x + 3x + 7x = 180°

15x = 180°

x = 180°/15

x = 12°

Now, ∠A = 5(12) = 60°

∠B = 3(12) = 36°

∠C = 7(12) = 84°

We observe that all the angles are less than 90 degrees.

Therefore, the given triangle is an acute angled triangle.

✦ Try This: The angles of a triangle are in the ratio 3 : 3 : 5. The triangle is

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 6

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NCERT Exemplar Class 9 Maths Exercise 6.1 Problem 4

The angles of a triangle are in the ratio 5 : 3 : 7. The triangle is a) an acute angled triangle, b) an obtuse angled triangle, c) a right triangle, d) an isosceles triangle

Summary:

The angles of a triangle are in the ratio 5 : 3 : 7. The triangle is an acute angled triangle since the measure of all the angles is less than 90 degrees

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