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 .
