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

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°.

Answer 2

In the given image, the line m is parallel to n. The transversal t intersects the parallel lines.

Given that:

∠1 = 50⁰

∠2 = 42⁰

∠3 = 88⁰

∠4 = 88⁰

∠5 = 92⁰

In the given lines parallel to each other, transversal t forms corresponding angles.

In the given image, ∠3 and ∠4 are corresponding.

The angle congruence theorem states that two angles are supplementary to the same angle, then the two angles are congruent.

Thus, the given diagram follows the congruence theorem.

To know more about the congruence theorem, refer to the following link:

https://brainly.com/question/10677856