Question : In a triangle$\frac{AB}{AC}=\frac{BD}{DC}$, $\angle$B = 70° and $\angle$C = 50°, then $\angle$BAD =?

Option 1: 60°

Option 2: 20°

Option 3: 30°

Option 4: 50°

Question : In a triangle, ABC, BC is produced to D so that CD = AC. If $\angle BAD=111^{\circ}$ and $\angle ACB=80^{\circ}$, then the measure of $\angle ABC$ is:

Option 1: 31°

Option 2: 33°

Option 3: 35°

Option 4: 29°

Question : In $\triangle ABC, \angle B=90^{\circ}$ and AB : BC = 1 : 2. The value of $\cos A+\tan C$ is:

Option 1: $\frac{5+\sqrt{5}}{2 \sqrt{5}}$

Option 2: $\frac{1+\sqrt{5}}{2 \sqrt{5}}$

Option 3: $\frac{2 \sqrt{5}}{2+\sqrt{5}}$

Option 4: $\frac{2+\sqrt{5}}{2 \sqrt{5}}$

Question : In $\triangle$ ABC, $\angle$ C = 90$^{\circ}$. M and N are the midpoints of sides AB and AC, respectively. CM and BN intersect each other at D and $\angle$ BDC = 90$^{\circ}$. If BC = 8 cm, then the length of BN is:

Option 1: $6 \sqrt{3} {~cm}$

Option 2: $6 \sqrt{6} {~cm}$

Option 3: $4 \sqrt{6} {~cm}$

Option 4: $8 \sqrt{3} {~cm}$

Question : In $\triangle A B C $, AB and AC are produced to points D and E, respectively. If the bisectors of $\angle C B D$ and $\angle B C E$ meet at the point O, and $\angle B O C=57^{\circ}$, then $\angle A$ is equal to:

Option 1: 93°

Option 2: 66°

Option 3: 114°

Option 4: 57°