Question

Question 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-angled triangle
D) An isosceles triangle

Answer 1

The answer is A.
Given, the ratio of angles of a triangle is 5 : 3 : 7.
Let the angles of a triangle be $\angle A,\angle Band\angle C$
Then, $\angle A=5x,\angle B=3xand\angle C=7x$
In $\Delta$ ABC, $\angle A+\angle B+\angle C={180}^{\circ }$ [sum of all angles of a triangle is ${180}^{\circ }$]
$\therefore 5x+3x+7x={180}^{\circ }$
$\Rightarrow 15x={180}^{\circ }$
$\Rightarrow x=\frac{{180}^{\circ }}{15}={12}^{\circ }$
$\therefore \angle A=5x=5\times {12}^{\circ }={60}^{\circ }$
$\angle B=3x=3\times {12}^{\circ }={36}^{\circ }$
$\angle C=7x=7\times {12}^{\circ }={84}^{\circ }$
Since all angles angles are less than ${90}^{\circ }$, triangle is an acute angled triangle.