Question

Find x in the following figure

Answer 1

∠ 1 + 90° = 180° ( linear pair )

∠1 = 90°

∠AED + linear pair of ∠AED = 180° ( Linear pair )

∠AED = 90° .....(2)

∠CDE + linear pair of ∠CDE = 180°

∠CDE + 60° = 180°

∠CDE = 120° .....(3)

∠ABC + linear pair of ∠ABC = 180°

∠ABC + 40° = 180°

∠ABC = 140° ....(4)

Now, In the Pentagon ABCDE,

sum of all interior angles = 540°

==> ∠ABC + ∠CDE + ∠AED + ∠BAE + linear pair of ∠x = 540°

==> 140° + 120° + 90° + 90° + 180° - ∠x = 540°

==> ∠x = 620 - 540

==> ∠x = 80°

Hence, Value of x is 80°