Question : In a triangle ABC, $\angle A = 70^{\circ}, \angle B = 80^{\circ}$ and D is the incentre of $\triangle ABC. \angle ACB = 2 x^{\circ}$ and $\angle BDC = y^{\circ}$ The values of x and y, respectively, are:

Option 1: 15 and 130

Option 2: 15 and 125

Option 3: 35 and 40

Option 4: 30 and 150

Question : I is the incenter of a triangle ABC. If $\angle$ ABC = 65$^\circ$ and $\angle$ ACB = 55$^\circ$, then the value of $\angle$ BIC is: 

Option 1: 130$^\circ$

Option 2: 120$^\circ$

Option 3: 140$^\circ$

Option 4: 110$^\circ$

Question : $\angle A, \angle B$ and $\angle C$ are three angles of a triangle. If $\angle A- \angle B=15^{\circ}, \angle B - \angle C=30^{\circ}$, then $\angle A, \angle B$ and $\angle C$ are:

Option 1: $80^{\circ},60^{\circ},$ and $40^{\circ}$

Option 2: $70^{\circ},50^{\circ},$ and $60^{\circ}$

Option 3: $80^{\circ},65^{\circ},$ and $35^{\circ}$

Option 4: $80^{\circ},55^{\circ},$ and $45^{\circ}$

Question : $D$ is a point on the side $BC$ of a triangle $ABC$ such that $AD\perp BC$. $E$ is a point on $AD$ for which $AE:ED=5:1$. If $\angle BAD=30^{\circ}$ and $\tan \left ( \angle ACB \right )=6\tan \left ( \angle DBE \right )$, then $\angle ACB =$

Option 1: $30^{\circ}$

Option 2: $45^{\circ}$

Option 3: $60^{\circ}$

Option 4: $15^{\circ}$

Question : In an isosceles triangle $ABC$, $AB = AC$ and $\angle A = 80^\circ$. The bisector of $\angle B$ and $\angle C$ meet at $D$. The $\angle BDC$ is equal to:

Option 1: $90^\circ$

Option 2: $100^\circ$

Option 3: $130^\circ$

Option 4: $80^\circ$

Question : In $\triangle$ABC and $\triangle$DEF, $\angle$A = $55^{\circ}$, AB = DE, AC = DF, $\angle$E = $85^{\circ}$ and $\angle$F = $40^{\circ}$. By which property are $\triangle$ABC and $\triangle$DEF congruent?

Option 1: SAS property

Option 2: ASA property

Option 3: RHS property

Option 4: SSS property