The figures are not drawn to scale. PQ and MN are straight lines. Find

<x = 30

Step-by-step explanation:

We can first calculate what <MOP is by doing 180 - 120 = 60, since line MN is 180 degrees and <PON is 120 degrees. Now we know that <MOP is 60 degrees, we can now plug in an equation to find what <x is. We know that line MN is 180 degrees, <MOR is 90 degrees, and <MOP is 60 degrees, we can do:

<x + 60 + 90 = 180

<x = 180 - 60 - 90

<x = 30

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°