Question

The measure of one angle of a right triangle is 56∘ more than the measure of the smallest angle. Find the measure of the smallest angle.

Answer 1

The smallest angle is 17°

Explanation:

All the angles add up to 180°. Use this to write an equation.

x = smallest angle

x+56 = not the smallest angle

90 = the right angle

x + x+56 +90 =180

combine like terms

2x + 146 = 180

subtract 146

2x = 34

divide by 2

x = 17

The smallest angle is 17°.

see image.

Answer 2

Subtract 90 from 180, which is 90 degrees.

Then you get the equation of 2x+56 = 90 for which the 2 represents the split between the 90 degrees and the +56 is the 56 degrees higher than the smaller angle.

Solving this gives you x = 17 degrees, which is the small angle.

For 17+56 = 73 = larger angle

17+73 = 90 plus the other 90 gives you 180 total.