Question

Find the values of the variables. Show your work and explain your steps. The diagram is not to scale.

Answer 1

Answer:

w=59 y=59 z=53 x=121 v=121

Step-by-step explanation:

inside a triangle the angles should add up to 180 so you can easily do 180-31 -90 to find w then with that you can find the rest and also w is equal to y cause theyre vertical angles

Answer 2

Answer:

w=59, x=121, v=121, y=59, and z=53

Step-by-step explanation:

One thing that all triangles have in common is that the sum of all of their angles is equal to 180 degrees.  This will help us solve for the variables.  

The triangle seen on the left side of the diagram is a right triangle, meaning that one of the angles is equal to 90 degrees.  The other angle is labeled as being 31 degrees, so we can add 90 and 31 together to get 121 degrees, which we can now subtract from 180 to get the angle w, which is 59 (180-121=59).

Knowing that w is equal to 59 degrees, we can solve for x because it is clear that this is a straight line, and these are equal to 180 degrees as well, so 180-59=x which is 121.

x and v are equal to each other as is w and y, so all that's left to solve for is z.

Triangles are equal to 180 degrees, so we subtract the sum of 68 and y (59) to get the measurement of z. 68+59=127.  180-127=53.  

I hope that this helps :)