Question : The ratio of the angles of a triangle is 1 : 2 : 6. What is the smallest angle?

Option 1: $40^\circ$

Option 2: $45^\circ$

Option 3: $30^\circ$

Option 4: $20^\circ$

Question : If $ABCD$ is a cyclic quadrilateral with $\angle A=50^{\circ},\angle B=80^{\circ}$, then $\angle C$ and $ \angle D$ are:

Option 1: $100^{\circ}$ and $130^{\circ}$

Option 2: $115^{\circ}$ and $115^{\circ}$

Option 3: $110^{\circ}$ and $120^{\circ}$

Option 4: $130^{\circ}$ and $100^{\circ}$

Question : In a $\triangle$ ABC, BC is extended to D and $\angle$ ACD = $120^{\circ}$. $\angle$ B = $\frac{1}{2}\angle$ A. Then $\angle$ A is:

Option 1: $60^{\circ}$

Option 2: $75^{\circ}$

Option 3: $80^{\circ}$

Option 4: $90^{\circ}$

Question : In $\triangle ABC$, the internal bisectors of $\angle B$ and $\angle C$ meet at point $O$. If $\angle A = 80^\circ$, then $\angle BOC$ is equal to:

Option 1: $100^\circ$

Option 2: $120^\circ$

Option 3: $130^\circ$

Option 4: $140^\circ$

Question : $O$ is the orthocentre of triangle $ABC$, and if $\angle BOC = 110^\circ$, then $\angle BAC$ will be:

Option 1: $110^\circ$

Option 2: $70^\circ$

Option 3: $100^\circ$

Option 4: $90^\circ$