Question : In $\triangle $ABC, AD$\perp$ BC and AD² = BD × DC. The measure of $\angle$ BAC is:

Option 1: 60°

Option 2: 75°

Option 3: 90°

Option 4: 45°

Question : The side $BC$ of a triangle $ABC$ is extended to $D$. If $\angle ACD = 120^{\circ}$ and $\angle ABC = \frac{1}{2} \angle CAB$, then the value of $\angle ABC$ is:

Option 1: $80^{\circ}$

Option 2: $40^{\circ}$

Option 3: $60^{\circ}$

Option 4: $20^{\circ}$

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: $90^\circ$

Question : $ABC$ is an isosceles triangle with $AB = AC$, The side $BA$ is produced to $D$ such that $AB = AD$. If $\angle ABC = 30^{\circ}$, then $\angle BCD$ is equal to:

Option 1: $45^{\circ}$

Option 2: $90^{\circ}$

Option 3: $30^{\circ}$

Option 4: $60^{\circ}$

Question : In triangle ABC, $\angle$ABC = 15°. D is a point on BC such that AD = BD. What is the measure of $\angle$ADC (in degrees)?

Option 1: 15

Option 2: 30

Option 3: 45

Option 4: 60