Question

In figure, ABC is an isosceles triangle whose side AC is produce
to E and through C, CD is drawn parallel to BA. Find the value of x.
​

Answer 1

Answer:

52° + 52° = 104°

Hence the solution of x is (d) 104°

Answer 2

Answer:

(d) 104°

Step-by-step explanation:

In ∆ABC, AB = AC

AC is produced to E

CD || BA is drawn

∠ABC = 52°

∴ ∠ACB = 52° (∵ AB = AC)

∴ ∠BAC = 180°-(52° +52°)

= 180°-104° = 76°

∵ AB || CD

∴ ∠ACD = ∠BAC (Alternate angles)

= 76°

and ∠BCE + ∠DCB = 180° (Linear pair)

∠BCE + 52° = 180°

⇒∠BCE = 180°-52°= 128°

∠x + ∠ACD = 380°

⇒ x + 76° = 180°

∴ x= 180°-76°= 104°