What do you know about the measure of the acute angles of a right triangle?
68^(∘) and 22^(∘)
Practice makes perfect
Let's illustrate our right triangle in a diagram.
Examining our diagram, ∠C, is going to be the angle that's 4 times the difference of the other acute angle and 5. Thus, the phrase "the measure of the other acute angle" refers to the smaller of the non-right angles, ∠B. Now we know enough to translate the verbal expression into a mathematical one:
4 times the difference of the measure
of the other acute angle and 5
4( m∠B - 5^(∘))
Hence, this expression equals the measure of ∠C. According to the Corollary to the Triangle Sum Theorem, the acute angles of a right triangle are complementary. This means the non-right angles add up to 90^(∘).
m∠B+m∠C=90^(∘)
Since we have an expression for m∠C in terms of m∠B, we can substitute m∠C with this expression and solve for m∠B.
