The measure of one angle of a right triangle is 42 ∘ more than the measure of the smallest angle. Find the measures of all three angles

Question

The measure of one angle of a right triangle is 42∘ more than the measure of the smallest angle. Find the measures of all three angles

Answer 1

To start this problem we know that the 3 angles of the triangle add up to 180 degrees and since the triangle is a right triangle that tells us that one angle is 90 degrees. 180-90=90 so the remaining 2 angles have to add up to 90 degrees.

If we set the smallest angle = x, then the other angle is x+42 since the measure is 42 degrees more than the smallest angle.

we can now add these 2 angles and set them = 90 degrees.

x+x+42=90

solving this for x we get x=24. Since we set the smaller angle equal to x then we know the smaller angle = 24 degrees. We find the other angle by adding 42 to the smaller angle: 24+42=66 degrees.

So our three angles are: 90, 66, and 24 degrees.

As a check: 90+66+24 does indeed equal 180.

Hope this helps!