Answer:
Step-by-step explanation:
This is a special right triangle that has 30, 60 and 90 degress corners. Because it is a special triangle, it also has side length values which always consistent relationship with one another.
Side opposite the 30° angle: x
Side opposite the 90° angle: 2x
So, 
Then use Pythagorean theorem. 
Answer:
Step-by-step explanation:
1)
O = center of circle (origin)
we know that the angle at the center of the circle ∠ ROS will be
180= 2(31) + ∠x
180-62 = ∠x
118° = ∠x
The supplemental angle to the 118° will be 62°
62° is the interior angle to arc QR , so
arc QR is also 62°
3)
b/c the intercepted arc YZ = 2* 68=136
then 136+125+? = 360
? = 99°
arc ZX = 99°
5)
O= center point
we are given the two arcs 120 and 70 for both of these we know that the
interior angles will be the same. ∠JOX has a central angle of 120 , then
b/c triangle JOX is an isosceles, we know that the two angles J and X of
the triangle JOX will be 1/2 of 60 , or 30 each
also for
also ∠XOY has an interior angle of 70 so the two angle at X and Y will be 1/2 of 110 , or 55°
now add 55+30 to find X for box XYZJ
85° = ∠X
