Question

The measures of the angles of a triangle are in the ratio 4 : 5 : 9. The triangle is:

• A. An acute angled triangle
• B. A right angled triangle
• C. An obtuse angled triangle
• D. None of the above

Answer 1

Answer: (B)

A right angled triangle

let the angles be $4x,5x$ and $9x$

$4x+5x+9x={180}^{\circ }18x={180}^{\circ }\Rightarrow x={10}^{\circ }$

So the angles are

$4\times {10}^{\circ }={40}^{\circ }5\times {10}^{\circ }={50}^{\circ }9\times {10}^{\circ }=90$

One of the angle is ${90}^{\circ }$, so the triangle is right angled triangle.