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: $90^{\circ}$

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 : 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 : The ratio of the angles of a triangle is 2 : 2 : 5. What is the largest angle?

Option 1: $120^\circ$

Option 2: $80^\circ$

Option 3: $110^\circ$

Option 4: $100^\circ$

Question : The internal bisectors of the angles B and C of a triangle ABC meet at I. If $\angle$BIC = $\frac{\angle A}{2}$ + X, then X is equal to:

Option 1: $60^{\circ}$

Option 2: $30^{\circ}$

Option 3: $90^{\circ}$

Option 4: $45^{\circ}$