Question : The exterior angles obtained on producing the base $BC$ of a $\triangle ABC$ in both ways are $120^{\circ}$ and $105^{\circ}$, then the vertical $\angle A$ of the triangle is:

Option 1: $36^{\circ}$

Option 2: $40^{\circ}$

Option 3: $45^{\circ}$

Option 4: $55^{\circ}$

Question : In an isosceles triangle, if the unequal angle is 4 times the sum of the equal angles, then each equal angle is:

Option 1: $25^{\circ}$

Option 2: $30^{\circ}$

Option 3: $21^{\circ}$

Option 4: $18^{\circ}$

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 : Three angles of a triangle are $(x-15^{\circ}),(x+45^{\circ}),$ and $(x+60^{\circ})$. Identify the type of triangle.

Option 1: Obtuse angle triangle

Option 2: Right angle triangle

Option 3: Isosceles triangle

Option 4: Equilateral triangle

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: $20^{\circ}$