smc

Question

In the ABC shown, D is some interior point, and x, y, z, w are the measures of angles in degrees. Solve for x in terms of y, z and w. FIGURE

Accepted Answer

By angles in a quadrilateral, x = 360^ - reflex ADB - y - z, and by angles at a point, reflex ADB = 360^ - w, so our expression becomes 360^ - (360^ - w) - y - z = w - y - z, which is w-y-z.