We want to find the measure of ∠ 4. To do so, notice that ∠ 4 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 the Corollary 4.1 of the Triangle Angle-Sum Theorem to find the desired measure.
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∠ 4 and the other acute angle has to be 90^(∘). Let's use this information to find the value of ∠ 4.
m∠ 4 + 35 ^(∘) = 90 ^(∘) → m∠ 4 = 55^(∘)
Extra
Pair of Angles
Pairs of angles can be classified in different ways depending on how their measures relate. Let's see this classification in the following table!
Pair of Angles
Complementary Angles
Two angles whose measures add up to 90^(∘) or π2 radians.
