Question

In the given figure, if $\angle$ACB = ${30}^{\circ }$, what is the value of $\angle$ACD in degrees?

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Answer 1

Construction: Join points B and D. Since AB = AD, $\angle$ABD = $\angle$ADB------------1

Also, BC = CD. So, $\angle$CBD = $\angle$CBD-------------2

Adding 1 and 2, We get $\angle$ABD + $\angle$CBD = $\angle$ADB + $\angle$CDB

$\angle$ABC = $\angle$ADC-------------------3

In $△$ABC and $△$ADC

AB = AD (Given)

$\angle$ABC = $\angle$ADC (Form 3)

BC = DC (Given)

By SAS congruency condition, $△$ABC $\cong$ $△$ADC

So, $\angle$ACB = $\angle$ACD = ${30}^{\circ }$ (Corresponding parts of congruent triangles)