Question

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

Answer 1

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`