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:

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:

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:

Question : In $\triangle \mathrm{ABC}, \angle \mathrm{A}=5 \mathrm{x}-60^{\circ}, \angle \mathrm{B}=2 \mathrm{x}+40^{\circ}, \angle \mathrm{C}=3 \mathrm{x}-80^{\circ}$. Find $\angle \mathrm{A}$.

Question : Let ABC be a right-angled triangle where $\angle \mathrm{A}=90^{\circ}$ and $\angle \mathrm{C}=45^{\circ}$. Find the value of $\sec \mathrm{C}+\sin \mathrm{C} \sec \mathrm{C}$.