Question

Prove that the sum of the three angles of a triangle is two right angles. If in a right angles triangle an acute angle is 1/4th the other, find the acute angles.

Answer 1

As we know that the sum of all the three angles of a triangle is ${180}^{\circ }$ and a right angle is ${90}^{\circ }$.

Number of right angles in a triangle $=\frac{{180}^{\circ }}{{90}^{\circ }}=2$

Hence proved.

Say $X=$ smaller acute angle in right triangle
$4X=$ larger acute angle
${90}^{\circ }=$ right angle
$x+4x+{90}^{\circ }=180$
$5x={90}^{\circ }$
$x={18}^{\circ }$
$4x={72}^{\circ }$
Acute angles are ${18}^{\circ }$ and ${72}^{\circ }$