Mathematics

Grade9

Easy

Question

# The steps of the proof are shown.

Given:

PROVED:

1. m ∠ 1 + m ∠ 2 = 180 (Given)

2. m ∠ 1 = 62 (_____)

3. 62 + m ∠ 2 = 180 (Substitution Property)

4. m ∠ 2 = 118 (_____)

What is the reason for step 2 and step 4?

- 2- Subtraction Property, 4- Subtraction Property
- 2- Given, 4- Subtraction Property
- 2- Distributive Property, 4- Substitution Property
- 2- Given, 4- Substitution Property

Hint:

### In this question , given is m∠1 + m∠2 = 180° . And also m∠1 = 62° and here proved is m∠2 =118°. Here we have to find the reason for step 2 and step 4. Remember the property of equality.

## The correct answer is: 2- Given, 4- Subtraction Property

### Here we have to find the reason for step 2 and step 4 .

The given is m∠1 + m∠2 = 180° , And also m∠1 = 62°.

Now ,

m∠1 + m∠2 = 180° ( given)

m∠1 = 62° ( given)

62 + m∠2 = 180° ( substitution property )

m∠2 =118° ( subtraction property )

Therefore, the reason of step 2 and step 4 is given and subtraction property.

The correct answer is 2- Given , 4- Subtraction property.

Or, simply

The whole proof:

m ∠ 1 + m ∠ 2 = 180 (Given)

m ∠ 1 = 62 (Given)

62 + m ∠ 2 = 180 (Substitution Property)

m ∠ 2 = 180 - 62 = 118 (Subtraction Property)

In this question, we have to step 2 and step 4 reason . For that we must know the property or equality. Here step 2 is given but step 4 is subtraction property. In subtraction property, if A=B , then A – x = B – x .