Question

Calculate x :

Answer 1

Let triangle be ABC and altitude be AD.

In ΔABD,
∠DBA = ∠DAB = 50° ...[Given BD = AD and angles opposite to equal sides are equal]
Now,
∠CDA = ∠DBA + ∠DAB ...[Exterior angle is equal to the sum of opp. interior angles]
∴ ∠CDA = 50° + 50° 
⇒ ∠CDA = 100°

In ΔADC,
∠DAC = ∠DCA = x  ...[Given AD = DC and angles opposite to equal sides are equal]
∴ ∠DAC + ∠DCA + ∠ADC = 180°
⇒ x + x + 100° = 180°
⇒ 2x = 80°
⇒ x = 40°