The measurement of the smallest angle in a right triangle is 45° less than the measure of the next larger angle. find the measures of all three angles.

Hey there!

The interior angles of a triangle always have to add up to 180 degrees.

We are told that this is a right triangle, so one of the angles must be 90 degrees. This means that the measures of the other two angles must add up to 90.

90 + m<1 + m<2 = 180

If the smallest angle is 45 degrees less than the next largest angle, the only option for this would be for both of the remaining angles to be 45 degrees. The next largest angle would be the right angle, and 90 -  45 = 45.

We can't have any of the other angles be more than 90 degrees because then it wouldn't be a proper triangle.

So, the measures of the angles are going to be 90, 45, and 45.

Hope this helps!