Question

PLEASE HELP!!!Mary is explaining the angle relationship of the interior angles of triangles to a coworker. She states that the angles should always add up to 180°. How can Mary prove that this is true? (Hint: Imagine taking the angles and putting them side by side.)

Answer 1

Answer with explanation:

To Prove: Sum of Interior angles of triangle is 180°.

Proof:

  In ΔABC

Draw line l, parallel to BC.

∠1=∠2------(1)

∠3=∠4------(2)

As lines are parallel , So Alternate Interior angles are equal.

→→Angles, ∠1,∠3, and ∠5 lie on a line.That, is they form a linear pair.Sum of Angles in linear pair is 180°.

 ∠1+∠3+∠5=180°

→∠2+∠4+∠5=180°-------[Using 1 and 2]

⇒∠A + ∠B+ ∠C=180°

Answer 2

I think it’s this... Because angles on a straight line add to 180 degrees and if you were to take the interior angles and put them next to each other, they would make a straight line, therefore they would have to add to 180 degrees .