Answer:
m∠4 = 54°
m∠1 = 126°
Step-by-step explanation:
m∠6 ≅ 54° → given
∠6 ≅ ∠8 → vertical angles are congruent
∠8 ≅ ∠4 → corresponding angles are congruent
∠6 ≅∠4 → transitive property
m∠6 = m∠4 → definition of congruence (if they are congruent, their measures are equal)
m∠4 = 54° → transitive property
∠4 and ∠1 are linear pairs → given
∠4 and ∠1 are supplementary → definition of linear pairs
m∠4 + m∠1 = 180 → definition of supplementary angles
m∠1 = 126° → subtraction
I realize this is not the most efficient way to go about it, but it works!
My way of proving can be a little weird, so feel free to ask for clarification!
