Question

Based on the figure, which of the following statements
CANNOT be proven?

Answer 1

• 4th option : m∠1 + m∠3 = m∠2 + m∠4

Explanation:

By VOA theorem, vertically opposite angles are equal.

• ∠1 = ∠3
• ∠2 = ∠4

⇒ You can write : ∠1 + ∠2 = ∠3 + ∠4

⇒ or ∠4 - ∠1 = ∠3 - ∠2

⇒ The 4th option does not give it correctly

Answer 2

the final one

Explanation:

to figure this equation out it is easier to add numbers to the angles

for 1 we can have it as 100 and for 2 we can have it as 80

that means 3 is 100 and 4 is 80

100 - 80 is also 100 - 80 so the first one can be proven

100 + 80 = 180 so the second one can be proven

80 = 80 so the third one can be proven

80 + 80 = 100 + 100 is not correct because it turns into 160 = 200 which is incorrect so the last one cannot be proven