#1**+4 **

a.

On this one:

∠A and ∠B are both on the circle and intercept the same arc...so they have the same measure.

∠B = 41º

the third angle in the lower triangle = 180º - (38º + 41º) = 101º

and m∠x = 180º - 101º = 79º

hectictar
May 4, 2017

#2**+2 **

Here's b

The vertical angle to x has the same measure....and the endpoints of this angle have the same endoints as the inscribed angle having the measure of 15°.....so the arc intercepted by both angles will be 30°

And the measure of the angle formed by 2 chords that intersect inside the circle is 1/2 the sum of the chords' intercepted arcs.

So.....x = (1/2) (46° + 30°) = (1/2) (76°) = 38°

CPhill
May 4, 2017

#3**+2 **

Here's c

The vertical angle to the 50° angle will have its endpoints on arc "x".....since both of these are central angles, then "x" has the same 50° measure

And z is an inscribed angle intercepting this 50° arc....so its measure is (1/2) of this = 25°

And using the same intercepting chord theorem as above, y = (1/2)(70° + 50°) =

(1/2) (120° ) = 60°

CPhill
May 5, 2017