Accepted Solution

It would help if they put some labels on the picture.y looks easy.  We do that first.   The subtended angle is half the central angle, so half the arc measure.  SoAnswer: y  = 23 degreesOK, z next.  Clearly the figure isn't to scale; compare that 34 degrees and the 46 degrees.   Anyway, it's 360 degrees around the circle, so that leavesz = 360 - (160+46+34) = 120Answer: z = 120 degreesx is not really determined unless that we're supposed to assume that where the left side touches the circle is a tangent.   Let's call that point T.  Let's call X and Y the vertices near x and y on the figure.  We'll call the center C. Clearly we can extend the base XY of the triangle, call the endpoint X and connect T to it.  So unless we have the tangent constraint or something else, x isn't determined.So we'll assume XT is tangent to the circle.  Angle TYX, the vertex by y, is half of 46+34, so TYX=40 degrees.  TCY is an isosceles triangle, two radii for sides.  Angle TCY=160 degrees. so CYT=CTY=10 degrees.  The radius and the tangent make a right angle so that makes angle XTY=90+10=100.  We have XTY=100, TYX=40 so that leaves TXY=40, and the triangle in the figure is isosceles.Answer: x = 40 degrees