We want to find the measure of ∠ 1. To do so, notice that ∠ 1 is one of the acute angles of a right triangle. Since the measure of the other acute angle of this right triangle is given on the figure, we can use Corollary 4.1 of the Triangle Angle-Sum Theorem.
Corollary 4.1
The acute angles of a right triangle are complementary, so their measures add up to 90^(∘).
This means that the sum of m∠ 1 and the other acute angle has to be 90^(∘). Let's use this information to set up an equation for m∠ 1.
m∠ 1 + m∠ 5 = 90 ^(∘)
Now we will substitute m∠ 5 = 29^(∘) into the above equation and solve it for m∠ 1.
