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#.

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#