For question b work out the angle bxc give a reason for each angle you work out.

M∠BXC = 70°.

We start out with m∠XBC.  It is 55°, because it is a corresponding angle with ∠AXY.

Since ∠XBC and ∠XCB are the base angles of an isosceles triangle, they are congruent.  This means that m∠XCB = 55°.

To find the measure of ∠BXC, we find the sum of the two base angles in the isosceles triangle and subtract it from 180:

180-(55+55) = 180-110 = 70°