Step 1: Find angle YXZ. XW bisects angle YXZ, and angle WXZ = 40°. Angle YXZ = 2 × 40° = 80° Step 2: Find the base angles of the isosceles triangle. Since XY = XZ, triangle XYZ is isosceles, so angle XYZ = angle XZY. Angle XZY = (180° − 80°) ÷ 2 = 100° ÷ 2 = 50° Step 3: Find angle XWZ using the angle sum in triangle XWZ. In △XWZ: angle WXZ + angle XZW + angle XWZ = 180° 40° + 50° + angle XWZ = 180° Angle XWZ = 180° − 90° = 90° Step 4: Find angle XWY. Angles XWY and XWZ are supplementary (they form a straight line at W on YZ). Angle XWY = 180° − 90° = 90° Step 5: Find the required sum. Angle XWY + angle XZY = 90° + 50° = 140°