Answer:
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Step-by-step explanation:
Given
angle1 + angle2 = 180
angle3 + angle4 = 180
then angle1 + angle2 = angle3 + angle4 : substitution
angle1 - angle3 = angle4 - angle2 : subtracts angle 3 and angle 2 from both sides
It has been proven that m∠3 = m∠4 . Therefore angle 3 = angle 4
From the question
angle 1 and angle 4 form a linear pair
That is,
m∠1 + m∠4 = 180° ------- (1)
Also, from the question
angle 1 and angle 2 are supplementary
That is,
m∠1 + m∠2 = 180° ------- (2)
To prove that m∠3 = m∠4
First, we can observe that
m∠2 = m∠3 (Vertically opposite angle)
From equation (2)
We have that
m∠1 + m∠2 = 180°
Since, m∠2 = m∠3
∴ m∠1 + m∠3 = 180°
Now, from equation (1)
We have
m∠1 + m∠4 = 180°
Since, m∠1 + m∠3 = 180°
Then, we can write that
m∠1 + m∠3 = m∠1 + m∠4
Subtract m∠1 from both sides
m∠1 - m∠1 + m∠3 = m∠1 - m∠1 + m∠4
∴ m∠3 = m∠4
Hence, it has been proven that m∠3 = m∠4 . Therefore angle 3 = angle 4
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