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 : The side BC of a triangle ABC is produced to D. If $\angle ACD = 112^\circ$ and $\angle B =\frac{3}{4} \angle A$ then the measure of $\angle B$ is:

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 : In a $\triangle ABC$, if $2\angle A=3\angle B=6\angle C$, then the value of $\angle B$ is:

Question : In $\triangle$ABC, $\angle$A = $90^{\circ}$, BP and CQ are two medians. Then the value of $\frac{BP^2 + CQ^2}{BC^2}$ is: