From the figure, we can identify a number of vertical angles.
&∠1 and ∠5
&∠2 and 40^(∘)
&∠3 and 30^(∘)
According to the Vertical Angles Congruence Theorem, vertical angles are congruent. Therefore, we know that ∠1≅ ∠5, m∠2=40, and m∠3=30^(∘). Let's show this in our diagram. Note that ∠1 is a right angle and therefore measures 90^(∘).
To find the remaining m∠4, notice that 30^(∘), 40^(∘), and ∠4 in the figure below make up a right angle.
By adding these three angle measures and setting their sum equal to 90^(∘), we can solve for m∠4.
