(a) First, note that the angle ∠PLN is equal to x°. Therefore 2x° = 180° - 120° ⇒ x = 30°. Next, note that ∠PLM = 90° - ∠PLN = 90° - x° = 60° and that ∠LPM = 180° - 120° = 60°. Therefore y = 180° - 60° - 60° = 60°.
(b) Note that triangle XRY is equilateral, therefore all its angles are 60°. Next note that y° = ∠XRY = 60°. Finally, x° = 180° - ∠ XYR - y° = 60°.
(c) y° = ∠CDB = 20°. Finally, 2x° = 180° - 20° ⇒ x° = 80°.
