Since lines l and m are parallel, the measure of each angle include;
m∠b = 138°
m∠c = 42°
m∠d = 138°
m∠e = 42°
m∠f = 138°
m∠g = 42°
m∠h = 138°
m∠e ≅ m∠g (vertical angles theorem)
m∠g = 42°
In Mathematics, the linear pair theorem states that the measure of two angles would add up to 180° provided that they both intersect at a point or form a linear pair.
By applying the linear pair theorem to parallel lines l and m, we can logically deduce the following supplementary angles:
m∠a + m∠b = 180°
m∠b = 180° - 42
m∠b = 138°
m∠b ≅ m∠d (vertical angles theorem)
m∠d = 138°
m∠c ≅ m∠a (vertical angles theorem)
m∠c = 42°
m∠e ≅ m∠a (corresponding angles theorem)
m∠e = 42°
m∠f ≅ m∠d (alternate interior angles theorem)
m∠f = 138°
m∠h ≅ m∠f (vertical angles theorem)
m∠h = 138°
m∠e ≅ m∠g (vertical angles theorem)
m∠g = 42°