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, 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: $65^{\circ}$

Question : In $\triangle A B C$ the internal bisectors of $\angle ABC$ and $\angle ACB$ meet at $X$ and $\angle BAC=30^{\circ}$. The measure of $\angle BXC $ is:

Option 1: $120^{\circ}$

Option 2: $115^{\circ}$

Option 3: $105^{\circ}$

Option 4: $150^{\circ}$

Question : In a triangle ABC; 8$\angle$A = 6$\angle$B = 3$\angle$C. What are the degree measures of $\angle$ A, $\angle$ B, and $\angle$C?

Option 1: $48^{\circ}, 96^{\circ}, \text{and } 36^{\circ}$

Option 2: $36^{\circ}, 96^{\circ}, \text{and } 48^{\circ}$

Option 3: $36^{\circ}, 48^{\circ}, \text{and } 96^{\circ}$

Option 4: $96^{\circ}, 48^{\circ}, \text{and } 36^{\circ}$

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