Here x + 60° = 180° (Linear pair)
⇒ x = 180° – 60° = 120°
Again, y + 100° = 180°
⇒ y = 180° – 100 = 80°
Similarly, z + 130° = 180°
⇒ z = 180° – 130° = 50°
We know that the sum of all interior angles of an n sided polygon is (2n – 4) right angle.
∴The sum of all interior angles of 5 sided polygon
= (2 x 5 – 4) x 90°
= 6 x 90°
= 540°
Let the remaining two angles of pentagon be a and b.
Then a + b + x + 100° + 130° = 540°
⇒ a + (180° – 85°) + 120° + 100° + 130° = 540°
⇒ a + 95° + 120° + 100° + 130° = 540°
⇒ a + 445° = 540°
⇒ a – 540° – 445° = 95°
∴w = 180° – a = 180° – 95°
⇒ w = 85°
