Question

Given: ∠22 and ∠24 are vertical angles.

Prove: ∠23 + ∠24 = 180°

Statements Reasons
m∠22 + m∠23 = 180 ∠22 and ∠23 are vertical angles
∠22 and ∠23 are a linear pair Definition of linear pair
∠23 and ∠24 are a linear pair Definition of linear pair
lines m and n intersect at P Given
m∠1 = m∠4 Alternate Interior Angles Theorem
Assemble the proof by choosing the correct Statements and Reasons.

a) 2, 3, 4, 1
b) 1, 2, 3, 4
c) 4, 3, 2, 1
d) 3, 2, 1, 4

Answer 1

To prove that ∠23 + ∠24 = 180°, we use the properties of vertical angles and linear pairs.

Step-by-step explanation:

To prove that ∠23 + ∠24 = 180°, we start with the given statement that ∠22 and ∠24 are vertical angles. Vertical angles are the angles opposite each other when two lines intersect. We know that the sum of the measures of the angles in a linear pair is 180°. Since ∠22 and ∠23 are also a linear pair, their measures add up to 180°.

Therefore, we can conclude that ∠23 + ∠24 = 180°.