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∘

Answer 1

Dear future people..... The answers are

1. Triangle Sum Theorem

2. Corresponding

3. Linear Pair Postulate

4. Subtraction Property of Equality

Answer 2

Triangle sum theorem; corresponding; linear pair postulate; subtraction property of equality.

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.