Question

if the angles of a triangle are in the ratio 5 : 3 : 7, what type of triangle is it?
a an acute angled triangle
b an obtuse angled triangle
c an equilateral triangle
d an isosceles triangle

Explanation:

Step1: Let the angles be 5x, 3x, 7x.

The sum of angles in a triangle is 180°. So, 5x + 3x+7x = 180°.

Step2: Combine like - terms.

15x = 180°.

Step3: Solve for x.

x = $\frac{180}{15}$ = 12°.

Step4: Find the angles.

The angles are 5×12° = 60°, 3×12° = 36°, 7×12° = 84°.

Step5: Classify the triangle.

Since all angles (36°, 60°, 84°) are less than 90°, it is an acute - angled triangle.

Answer:

A. an acute angled triangle