+912 Fill in the blank to correctly complete the proof.
Given: m ∥ n , m∠1= 50∘ , and m∠2 = 42∘
Prove: m∠5 = 92∘
It is given that m ∥ n , m∠1 = 50∘ , and m∠2 = 42∘. By the _______________, m∠3 = 88∘. Because ____________ angles formed by two parallel lines and a transversal are congruent, ∠3 ≅ ∠4 . By the angle congruence theorem, m∠3 = m∠4 . Using substitution, 88∘ = m∠4. Angles 4 and 5 form a linear pair, so by the ___________, m∠4 + m∠5 = 180∘ . Substituting gives 88∘+ m∠5 = 180∘ . Finally, by the ______________, m∠5 = 92∘.
OPTIONS: linear pair postulate, subtraction property of equality, transitive property of equality, triangle sum theorem, alternate interior, corresponding , alternate exterior
+2446 1) Triangle Sum Theorem
To find \(m\angle 3\), one must understand that the sum of the measures of all the interior angles of a triangle equals 180, which is what the triangle sum theorem states.
2) Corresponding
\(\angle 3\) and \(\angle 4\) are both corresponding angles because both angles maintain the relative positions at the intersection of two lines.
3) Linear Pair Postulate
4) Subtraction Property of Equality
The final step requires elementary subtraction to figure out the measure of the remaining angle.
+2446 1) Triangle Sum Theorem
To find \(m\angle 3\), one must understand that the sum of the measures of all the interior angles of a triangle equals 180, which is what the triangle sum theorem states.
2) Corresponding
\(\angle 3\) and \(\angle 4\) are both corresponding angles because both angles maintain the relative positions at the intersection of two lines.
3) Linear Pair Postulate
4) Subtraction Property of Equality
The final step requires elementary subtraction to figure out the measure of the remaining angle.
