Question : In $\triangle {ABC}$, O is the incentre and $\angle {BOC}=135^{\circ}$. The measure of $\angle {BAC}$ is:

Question : In a circle, O is the centre of the circle. Chords AB and CD intersect at P. If $\angle AOD=32^{\circ}$ and $\angle CO B=26^{\circ}$, then the measure of $\angle APD$ lies between:

Question : In $\triangle ABC$, M and N are the points on side BC such that AM $\perp$ BC, AN is the bisector of $\angle A$, and M lies between B and N. If $\angle B=68^{\circ}$, and $\angle \\{C}=26^{\circ}$, then the measure of $\angle MAN$ is:

Question : Two chords AB and CD of a circle with centre O intersect at P. If $\angle$ APC = 40º, then the value of $\angle$AOC + $\angle$BOD is:

Question : In an isosceles triangle, if the vertex angle is twice the sum of the base angle, then the measure of the half of the vertex angle of the triangle is: