Answer:
Triangle sum theorem; corresponding; linear pair postulate; subtraction property of equality.
Step-by-step explanation:
The triangle sum theorem states that the sum of measures of the angles of a triangle is always 180°. Since we have two of the angles, 50 and 42, we know that
m∠3 = 180-(50+42) = 180-(92) = 88
∠3 and ∠4 are corresponding angles; this means they are on the same side of the transversal and on the same side of their corresponding parallel line. Corresponding angles are congruent, so this means that ∠3≅∠4, which means that the measures of these two angles is equal.
The linear pair postulate states that if two angles form a linear pair, the sum of their measures is 180°.
To cancel the 88° in the last statement, we subtract it from each side; the subtraction property of equality is what allows this.
