Question

Line n ‖ line BC.

Which statements about the figure must be true?

Choose all answers that are correct.
A.
m∠1 = 45°

B.
m∠2 + m∠3 = 84°

C.
m∠2= 45°

D.
m∠3 = 45°

Answer 1

angle 2=45 degree
and angle 3=39 degree
because they are alternate interior angles
so B is a correct answer ->45+39=84

Answer 2

Let's take a look!

A. is wrong because, for any given straight line, all the angles on one side add up to 180. we know that n is a line because they said it was in the directions. to calculate angle 1, we take 45 +39 and subtract the answer from 180. Angle 1= 96 degrees

B. is correct, because there is a property that says when a transversal crosses two parallel lines, there will be corresponding with the same degrees. Because of this, we know that angle 2= 45 and angle 3=39. 45 +39 = 84, so B is true

C is also correct, due to the property/theorem/thingy previously mentioned that your math book should list somewhere if you are learning this.

D is incorrect, because of again aforementioned theorem. angle 3 + 39 degrees