Question

From the following figure,

prove that: ∠ACD = ∠CBE

Answer 1

In ΔACB,
AC = AC ....[Given]
∴ ∠ABC = ∠ACB  ...(i) [angles opposite to equal sides are equal]
∠ACD + ∠ACB = 180° ......(ii) [DCB is a straight line]
∠ABC + ∠CBE = 180°  ….(iii)[ ABE is a straight line ]
Equating (ii) and (iii)
∠ ACD + ∠ACB = ∠ABC + ∠CBE
⇒ ∠ACD + ∠ACB = ∠ACB + ∠CBE ......[From (i)]
⇒ ∠ACD = ∠CBE.