Question

Two angles of a triangle are equal and the third angle is greter than each of those angles by ${30}^{\circ }$. Determine all the angles of the triangle.

Answer 1

Let each of the two equal and angles = x

Then third angle = $x+{30}^{\circ }$

But sum of the three angles of a triangle is ${180}^{\circ }$

$\Rightarrow 3x+{30}^{\circ }={180}^{\circ }$
$\Rightarrow 3x={150}^{\circ }\Rightarrow x=\frac{{150}^{\circ }}{3}={50}^{\circ }$

$\therefore$ Each equal angle $={50}^{\circ }$

and third angle = ${50}^{\circ }+{30}^{\circ }={80}^{\circ }$

$\therefore$ Angles are ${50}^{\circ },{50}^{\circ }and{80}^{\circ }$