finding the value of each variable from a circle

[isu23pink]

Assume that lines that appear to be tangent. Find the value of each variable. If your answer is not an integer, round to the nearest tenth.
[attachment=2:1kgmoryc]no.8.jpg[/attachment:1kgmoryc]



also the second problem w/ the same directions i got wrong as well:
[attachment=1:1kgmoryc]20.jpg[/attachment:1kgmoryc]
i did:
1/2(92) = 41
180-41-90 = 49degress
WRONG.

third problem(w/ same directions), i got half right:
[attachment=0:1kgmoryc]17.jpg[/attachment:1kgmoryc]
x= 63degress
y= (180-63-46)
=71degres

never really understood how to do these types of problems, can someone help me?

 

[wjm11]

1) Tangents and radii form 90 degree angles. All quadrilaterals have 360 sum for interior angles.

2) Half of 92 is not 41.

 

[wjm11]

x= 63degress
y= (180-63-46)
=71degres

The arcs of a circle must add up to 360 degrees. It is not clear from the sketch if the 92 degrees refers to the arc or to the angle between two rays.

I will assume the angle between the two rays is 92.

92 + x + y = 180
y = 180 - 63 - 92