Answer: 64 degrees and Corresponding Angles Theorem and Linear Pair Theorem
If you start testing out every theorem then at a conclusion you will reach the answer of which theorem is used at first. So let's clear out all the theorem's
Alternate Interior Angle Theorem: States that, when two parallel lines are cut by a transversal , the resulting alternate interior angles are congruent.
So, in the figure below, if k ∥ l , then ∠2≅∠8 and ∠3≅∠5 . (the first image)
So in order to find angle 15, if we only use the Alternate Interior Angle Theorem then the match won't be finished so it is excluded.
Corresponding Angles Theorem: States that, when two parallel lines are cut by a transversal , the resulting corresponding angles are congruent.(2nd image)
So, if we follow this then we can find angle 16 only from angle 8. Another theorem is also mentioned with it so let's do that as well so that we see if it works out.
Linear Pair Theorem: If two angles form a linear pair, then the measures of the angles add up to 180°. (3rd image)
So if we know the value of angle 16 so if we subtract it from 180, then the value comes as the line is a straight line. So we can find angle 15 from it. Let's do the sum then,
As said angle 8 is corresponding to angle 16 so their values will be the same which is 116 degrees. Now subtract 116 from 180, 180-116 which is 64 degrees.
Just for more information:
Vertical Angle Theorem: If two angles form a linear pair, then the measures of the angles add up to 180°. Basically if two lines intersect then the opposite angles are equal.
Sorry for making it too long! And brainliest pwease if it is correct! <3 ~ ~ ~
