Question

Calculate the value of x in the given figure.

Answer 1

ANSWER:
Join A and D to produce AD to E.
Then,
∠CAD+∠DAB=55° and ∠CDE+∠EDB=x°
Side AD of triangle ACD is produced to E.
∴∠CDE=∠CAD+∠ACD ...i (Exterior angle property)
Side AD of triangle ABD is produced to E.
∴∠EDB=∠DAB+∠ABD ...ii (Exterior angle property)
Adding i and ii we get,∠CDE+∠EDB=∠CAD+∠ACD+∠DAB+∠ABD
⇒x°=∠CAD+∠DAB+30°+45°

⇒x°=55°+30°+45°

⇒x=130