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

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Answer 1 · 2014-11-26T19:39:37

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

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

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

Applying these conditions, we can say that,

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

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

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

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

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 $25^{o}$ $25^o$ , the other acute angle is given by:

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