Question : $\triangle ABC$ is an equilateral triangle. The side $BC$ is produced to point $D$. If $A$ joines $D$ and $B C=CD$, then the degree measure of angle $CAD$ is equal to:

Option 1: $30^{\circ}$

Option 2: $15^{\circ}$

Option 3: $45^{\circ}$

Option 4: $18^{\circ}$

Question : The side $BC$ of a triangle $ABC$ is extended to $D$. If $\angle ACD = 120^{\circ}$ and $\angle ABC = \frac{1}{2} \angle CAB$, then the value of $\angle ABC$ is:

Option 1: $80^{\circ}$

Option 2: $40^{\circ}$

Option 3: $60^{\circ}$

Option 4: $20^{\circ}$

Question : In a $\triangle$ ABC, BC is extended to D and $\angle$ ACD = $120^{\circ}$. $\angle$ B = $\frac{1}{2}\angle$ A. Then $\angle$ A is:

Option 1: $60^{\circ}$

Option 2: $75^{\circ}$

Option 3: $80^{\circ}$

Option 4: $90^{\circ}$

Question : $ABC$ is an isosceles triangle with $AB = AC$, The side $BA$ is produced to $D$ such that $AB = AD$. If $\angle ABC = 30^{\circ}$, then $\angle BCD$ is equal to:

Option 1: $45^{\circ}$

Option 2: $90^{\circ}$

Option 3: $30^{\circ}$

Option 4: $60^{\circ}$

Question : In a $\triangle ABC$, if $2\angle A=3\angle B=6\angle C$, then the value of $\angle B$ is:

Option 1: $60^{\circ}$

Option 2: $30^{\circ}$

Option 3: $45^{\circ}$

Option 4: $90^{\circ}$