Answer: B) m∠3 + m∠5 = 180°
Step-by-step explanation:
Concept:
For this question, we will be looking at each answer choice and eliminating the incorrect ones
A) ∠1 ≅ ∠6
∠1 is an exterior angle
∠6 is an interior angle
They are in an alternative position
Since they are neither both exterior nor interior, they are not congruent
[tex]\large\boxed{FALSE}[/tex]
B) m∠3 + m∠5 = 180°
∠3 is an interior angle
∠5 is an interior angle
They are in a same-side position
Since they are both interiors, they fulfill the same-side interior angle theorem, which states: that if a transversal cuts two parallel lines, then the interior angles on the same side of the transversal are supplementary, which means their sum adds up to 180°.
[tex]\Huge\boxed{TRUE}[/tex]
C) m∠2 + m∠6 = 180°
∠2 is an exterior angle
∠6 is an interior angle
They are in a same-side position
Since they are on the same side, they fulfill the corresponding angle theorem which states: the angles that occupy the same relative position at each intersection are congruent to each other.
However, they are only congruent, they don't add up to 180°
[tex]\large\boxed{FALSE}[/tex]
D) ∠4 ≅ ∠8
∠4 is an interior angle
∠8 is an exterior angle
They are in an alternative position
Since they are neither both exterior nor interior, they are not congruent
[tex]\large\boxed{FALSE}[/tex]
Hope this helps!! :)
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