Question : $\triangle \mathrm{ABC}$ and $\triangle \mathrm{DEF}$ are two triangles such that $\triangle \mathrm{ABC} \cong \triangle \mathrm{FDE}$. If AB = 5 cm, $\angle$B = 40° and $\angle$A = 80°, then which of the following options is true?

Option 1: DF = 5 cm, $\angle$E = 60°

Option 2: DE = 5 cm, $\angle$F = 60°

Option 3:  DE = 5 cm, $\angle$D = 60°

Option 4: DE = 5 cm, $\angle$E = 60°

Question : In $\triangle A B C, \mathrm{BD} \perp \mathrm{AC}$ at $\mathrm{D}$. $\mathrm{E}$ is a point on $\mathrm{BC}$ such that $\angle B E A=x^{\circ}$. If $\angle E A C=46^{\circ}$ and $\angle E B D=60^{\circ}$, then the value of $x$ is:

Option 1: 72°

Option 2: 78°

Option 3: 68°

Option 4: 76°

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°

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 a $\triangle ABC$, D and E are two points on AB and AC respectively such that DE || BC, DE bisects the $\triangle ABC$ in two equal areas. Then the ratio DB : AB is:

Option 1: $1:\sqrt2$

Option 2: $1:2$

Option 3: $\left ( \sqrt2-1 \right ):\sqrt2$

Option 4: $\sqrt2:1$