Question

Drag and drop an answer to each box to correctly complete the proof.

Given: m∥nm∥n , m∠1=50∘m∠1=50∘ , and m∠2=42∘m∠2=42∘ .

Prove: m∠5=92∘
It is given that m∥nm∥n , m∠1=50∘m∠1=50∘ , and m∠2=42∘m∠2=42∘ . By the , m∠3=88∘m∠3=88∘ . Because angles formed by two parallel lines and a transversal are congruent, ∠3≅∠4∠3≅∠4 . By the angle congruence theorem, m∠3=m∠4m∠3=m∠4 . Using substitution, 88∘=m∠488∘=m∠4 . Angles 4 and 5 form a linear pair, so by the , m∠4+m∠5=180∘m∠4+m∠5=180∘ . Substituting gives 88∘+m∠5=180∘88∘+m∠5=180∘ . Finally, by the , m∠5=92∘m∠5=92∘ .

Answer 1

To prove that m∠5 is 92°, geometric theorems such as the Alternate Interior Angles Theorem, Corresponding Angles Postulate, and Linear Pair Postulate are employed in a parallel line system. Following a step-by-step reasoning aligning with these theorems and given angle measurements, we establish m∠5 as 92°.

Step-by-step explanation:

The question aims to prove that the measure of angle 5 is 92 degrees (°), given certain angles in a parallel line and transversal system. To fill in the missing statements for the provided geometric proof, we utilize various geometric theorems:

• Alternate Interior Angles Theorem: Since lines m and n are parallel, and if m∠1 equals 50°, then m∠3 will be equal to 50° as well because alternate interior angles are congruent.
• Corresponding Angles Postulate: With parallel lines, this postulate states that ∠3 is congruent to ∠4, and therefore m∠3 equals m∠4.
• Linear Pair Postulate: This postulate supports that ∠4 and ∠5 form a linear pair, and their measures add up to 180°, therefore if m∠4 is 88°, then m∠5 would be 180° - 88°, which is 92°.

By combining these theorems and postulates with the given information, we successfully complete the proof that demonstrates the measure of angle 5 is indeed 92°.

Answer 2

It is given that m ∥ n, m∠1 = 50° , and m∠2 = 42°. By the triangle sum theorem, m∠3 = 88°. Because corresponding 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. Angles 4 and 5 form a linear pair, so by the linear pair postulate, m∠4 + m∠5=180°. Substituting gives 88° + m∠5=180°. Finally, by the subtraction property of equality, m∠5 = 92°.