Question

In a triangle ABC, D is a point on BC, such that $\angle CAD=\angle B$.
Then

• A. $\angle ADC=\angle A$
• B. $\angle ADC=\angle B$
• C. $\angle ADC=\angle C$
• D. $\angle ADC=\angle ADB$

Answer 1

The correct option is A $\angle ADC=\angle A$

Given: $△ABC$, Point D on BC such that $\angle CAD=\angle B$
In $△ABC$
$\angle A+\angle B+\angle C=180$ ......I
In $△ACD$

$\angle CAD+\angle ADC+\angle C=180$.....II

Thus, from I and II

$\angle A+\angle B+\angle C=\angle CAD+\angle ADC+\angle C$

hence, $\angle A=\angle ADC$ (Since, $\angle CAD=\angle B$)