Question 14 short fillin Use the information diagram and pro

Question 14 (short fill-in)

Use the information, diagram, and proof of the Triangle Angle Sum Theorem to fill in the blanks.

?___[A]____ and ?2 are alternate interior angles.

?___[B]____ and ?3 are alternate interior angles.

?___[A]____ ??2

?___[B]____ ??3

m?___[A]____ +m?1=m?DBC

m?DBC+m?___[B]____ =m?DBE

m?___[A]____ +m?1+m?___[B]____ =m?DBE

m?___[A]____+m?1+m?___[B]____ =180°

m?2+m?1+m?3=180°

Enter the angle measure that correctly fills in the blanks labeled with ___[A]____ in the proof.

m D B E 4 5 1 2

In any straight line total angle is 180 ⁰ here straight line DBE angle is also 180 ⁰ means that Angle 4 + Angle 1 + Angle 5 = 180 ⁰. ------- (1)

Given that m || n so Alternate interior angles are same. So Angle 4 = Angle 2 and Angle 5 = Angle 3.

Subsitituting these in equation (1) we get Angle 1 + Angle 2 + Angle 3 = 180 ⁰.

Sum of all angles in any triangle is 180 ⁰.

Hence proved.