By the Vertical Angles Congruence Theorem, ∠ 4 and ∠ 2 are congruent. Therefore we have that
m∠ 4 =m∠ 2.
As m∠ 4 =88^(∘), it must follow that m∠ 4 =88^(∘). Supplementary angles have measures that sum to 180^(∘). Additionally, since we also know that ∠ 1 and ∠ 3 are vertical angles, we can write the following three equations:
m∠ 4+m∠ 1&=180
m∠ 4+m∠ 3&=180
m∠ 1&=m∠ 3.
By solving the first equation for m∠ 1, we also figure out the measure of ∠ 3.
