# How do you find all the missing angles, if you know one of the acute angles of a right triangle?

Nov 26, 2014

The sum of the measures of all the angles in a triangle is always equal to ${180}^{o}$.

In a right triangle, however, one of the angles is already known: the right angle, or the ${90}^{o}$ angle.

Let the other two angles be $x$ and $y$ (which will be acute).

Applying these conditions, we can say that,

$x + y + {90}^{o} = {180}^{o}$

$x + y = {180}^{o} - {90}^{o}$

$x + y = {90}^{o}$

That is, the sum of the two acute angles in a right triangle is equal to ${90}^{o}$.

If we know one of these angles, we can easily substitute that value and find the missing one.

For example, if one of the angles in a right triangle is ${25}^{o}$, the other acute angle is given by:

${25}^{o} + y = {90}^{o}$
$y = {90}^{o} - {25}^{o}$
$y = {65}^{o}$