Question

Calculate x :

Answer 1

Let the triangle be ABC and the altitude be AD.

In ΔABD,
∠DBA = ∠DAB = 37° .....[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 = 37° + 37° 
⇒ ∠CDA = 74°
Now in ΔADC,
∠CDA = ∠CAD = 74° ....[ Given CD = AC and angles opposite to equal sides are equal]
Now,
∠CAD + ∠CDA + ∠ACD = 180°
⇒ 74° + 74° + x = 180° 
⇒ x = 180° − 148° 
⇒ x = 32°