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 an isosceles triangle, if the unequal angle is five times the sum of the equal angles, then each equal angle is:

Option 1: $45^\circ$

Option 2: $60^\circ$

Option 3: $15^\circ$

Option 4: $30^\circ$

Question : In $\Delta ABC$, the external bisector of the angles, $\angle B$ and $\angle C$ meet at the point $O$. If $\angle A = 70^\circ$, then the measure of $\angle BOC$:

Option 1: $55^\circ$

Option 2: $75^\circ$

Option 3: $60^\circ$

Option 4: $50^\circ$

Question : If in a $\triangle ABC$, as drawn in the figure, $AB = AC$ and $\angle ACD = 120^{\circ}$, then angle A is equal to:

Option 1: $50^{\circ}$

Option 2: $60^{\circ}$

Option 3: $70^{\circ}$

Option 4: $80^{\circ}$

Question : In a triangle ABC, two angles A and B are equal. If the exterior angle is at $\angle A = 115°$, find the measure of $\angle C$.

Option 1: $50^{\circ}$

Option 2: $130^{\circ}$

Option 3: $115^{\circ}$

Option 4: $65^{\circ}$