Question

If, $△DCA\cong △BED$ by RHS criteria and $\angle$DBE = 30${}^{\circ }$, then, what is $\angle$CAD?

• A. 30°
• B. 45°
• C. 60°
• D. 90°

Answer 1

The correct option is C 60°

Since, $△DCA\cong △BED$
corresponding parts of the two triangles are equal.
So, $\angle$DBE = $\angle$ADC = 30${}^{\circ }$


So, in $△$DCA,
$\angle$DCA = 90°
$\angle$ADC = 30°

$\angle$CAD = 180° - ($\angle$DCA + $\angle$ADC)
($\because$ sum of all the internal angles of a triangle is 180°)

$\Rightarrow$ $\angle$CAD = 180° - (90° + 30°)
$\Rightarrow$ $\angle$CAD = 60°