Answer:
Part 1) The perimeter of triangle ABC is 24 units
Part 2)
Step-by-step explanation:
Part 1) we know that
The <u><em>Midpoint Theorem</em></u> states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side
see the attached figure to better understand the problem
so
Applying the midpoint theorem
step 1
Find the value of BC
---> because A is the midpoint
substitute the given value of AY
step 2
Find the value of AC
---> because B is the midpoint
substitute the given value of BZ
step 3
Find the value of AB
substitute the given value of XZ
step 4
Find the perimeter of triangle ABC
substitute
Part 2) Find the measure of angle y
step 1
Find the measure of angle z
we know that
The sum of the interior angles in a triangle must be equal to 180 degrees
so
solve for z
step 2
Find the measure of angle y
we know that
----> by supplementary angles (form a linear pair)
we have
substitute
solve for y