In the figure, a is greater than b by one third of a right angle. Find the values of a and b.
           

Given that a > b by of a right angle.
  a = b + × 90° ⇒ a = b + 30°
  But a + b = 180° (Linear pair axiom)
⇒ b + 30 + b = 180°
⇒ 2b + 30° = 180°
      ⇒ 2b = 180° -30°
      ⇒ 2b = 150°.
       ∴ b = 75°
        ∴ a = 180° -75°
             = 105°
∴ The measure of a = 105° and b = 75°.