Final answer:
The missing statement is “m∠1 + m∠2 = 180°”, thus the correct option is 4.
Step-by-step explanation:
The given statement is a proof of the theorem that states the sum of two angles of a triangle is 180°. To prove this, we need to show that the angles of the triangle which are m∠1, m∠2 and m∠5 add up to 180°. The proof has three statements given: m∠1 = m∠2, m∠2 = m∠5 and m∠5 + m∠2 = 180°. Combining the first two statements, we get that m∠1 = m∠5. This means that m∠1 + m∠2 = m∠5 + m∠2 which is equal to 180°, as given in the third statement. Therefore, the missing statement is “m∠1 + m∠2 = 180°”.
To prove this, we can also use a simple diagram. Draw a triangle ABC with angles m∠A, m∠B and m∠C. By the theorem, we know that the sum of the three angles of any triangle is 180°. This means that m∠A + m∠B + m∠C = 180°. Let us assume that m∠A = m∠B and m∠C = m∠5. This would mean that m∠A + m∠B + m∠5 = 180°. Since m∠A = m∠B, we can rewrite this as m∠A + m∠2 + m∠5 = 180° or m∠1 + m∠2 = 180°. This proves that the missing statement is “m∠1 + m∠2 = 180°”.