Question

Plz Help Medal+Fan


Which relationship is always true for the angles x, y, and z of triangle ABC?

A. x + z = y

B. y + z = x

C. x + y + z = 180 degrees

D. x + y + z = 90 degrees

Answer 1

Since x is external angle, y and z are interior angles, x = y + z will be true

Answer 2

Do you want a proof for this?

Answer 3

yes plz

Answer 4

So we know that the sum of the angles in a triangle is 180. This leads us to come up with y + z + ??? = 180, where ??? is the angle opposite of x (but since it shares the line with x, it's actual value is 180 - x). Work with that information.

Answer 5

Sure. Just a minute

Answer 6

Draw CD parallel to AB and AD parallel to BC

Answer 7

Since AB parallel to CD, angle B will be equal to angle DCE (corresponding angles). And also, angle A will be equal to angle ACD.

Answer 8

Angle C will be equal to angle C

Answer 9

In triangle ABC, A+B+C = 180 degrees. And also BCE is a straight line. So, BCE = 180 degrees that is angle C+ACD+DCE = 180 degrees

Answer 10

But ACE(ACD+DCE) is an exterior angle. So, ACE=A+B

Answer 11

thxxxxxxxxxx!! :)

Answer 12

You're welcome :)