Mathematics
Grade9
Easy

Question

The steps of the proof are shown.
Given: m angle 1 plus m angle 2 equals 180 to the power of ring operator end exponent
m angle 1 equals 62 to the power of ring operator end exponent
PROVED: m angle 2 equals 118 to the power of ring operator end exponent

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?

  1. 2- Subtraction Property, 4- Subtraction Property
  2. 2- Given, 4- Subtraction Property
  3. 2- Distributive Property, 4- Substitution Property
  4. 2- Given, 4- Substitution Property

hintHint:

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 .

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