Question

PLS HELP I WILL MARK BRAINLIEST TO CORRECT AND EXPLAIN ANSWERS!!!!!!!!!!!!!!!!!!!
(Two Questions)
Which relationship is always true for the angles r, x, y, and z of triangle ABC? (first picture)
x + z = y

180 degrees − x = r

x + y + z = 180 degrees

x + y + z = 90 degrees


The figure shows two parallel lines AB and DE cut by the transversals AE and BD: (second picture)

Which statement best explains the relationship between Triangle ABC and Triangle EDC ?

Triangle ABC is similar to triangle EDC , because m∠3 = m∠6 and m∠1 = m∠4

Triangle ABC is similar to triangle EDC , because m∠3 = m∠4 and m∠1 = m∠5

Triangle ABC is congruent to triangle EDC , because m∠3 = m∠4 and m∠1 = m∠5

Triangle ABC is congruent to triangle EDC, because m∠3 = m∠6 and m∠61 = m∠4

Answer 1

the first one the answer is 
x + y + z = 180 degrees
proof

the sum of all angles in the triangles is always equal to 180 degrees
(check lesson)
second one is 
Its Step 2; it should be m∠o + m∠p = 180 degrees (supplementary angles)

Answer 2

Answer:

1. B

2.B

Step-by-step explanation:

We are given that a triangle ABC with angles r,x,y and z

We have to find the relationship is always true for the angles r,x,y and z of triangle ABC.

From given figure

$r+y+z=180^{\circ}$

$r+x=180^{\circ}$

$r=180-x$

Substitute the value of r then we get

$180-x+y+z=180$

$x=y+z$

Hence, option B is true.

2.We are given that two parallel lines AB and DE cut by the transversals AE and BD.

We have to find the best statement which explains the relationship between triangle ABC and triangle EDC

$m\angle 1=m\angle 5$ ( alternate interior angles )

$m\angle 2=m\angle 6$  ( Alternate interior angle )

$m\angle 3=m\angle 4$  (Vertical opposite angle )

Triangle ABC and triangle EDC are similar because $m\angle 3=m\angle 4,m\angle 1=m\angle 5$.

Therefore, option B is true.