Question

From the figure, which among the following is correct?

• A. $\angle ACD=\angle CBE$
• B. $\angle ACD=\angle CEB$
• C. $\angle ACD=\angle CAD$
• D. $\angle ADC=\angle CBE$

Answer 1

The correct option is A $\angle ACD=\angle CBE$

Given,
In $\Delta ACB$
AC = AB
$\angle ACB=\angle ABC$ .. (i)
[Angles opposite to equal sides are equal]
$\angle ACD+\angle ACB={180}^{\circ }$ .. (ii) [Straight Angle]
$\angle ABC+\angle CBE={180}^{\circ }$ ..(iii)
[Straight Angle]

Equating (ii) and (iii),
$\angle ACD+\angle ACB=\angle ABC+\angle CBE$
$\angle ACD+\angle ABC=\angle ABC+\angle CBE$ [From (i)]
$\angle ACD=\angle CBE$