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

Question : In $\triangle$ABC, $\angle$A = $\angle$B = 60°, AC = $\sqrt{13}$ cm, the lines AD and BD intersect at D with $\angle$D = 90°. If DB = 2 cm, then the length of AD is:

Option 1: 3 cm

Option 2: 3.5 cm

Option 3: 4 cm

Option 4: 4.7 cm

Question : In $\triangle ABC$, the internal bisectors of $\angle ABC$ and $\angle ACB$ meet at $I$ and $\angle BAC=50°$. The measure of $\angle BIC$ is:

Option 1: $105°$

Option 2: $115°$

Option 3: $125°$

Option 4: $130°$

Question : In $\Delta ABC,\angle BAC=90^{\circ}$ and D is the mid-point of BC. Then which of the following relations is true?

Option 1: $AD=BD=CD$

Option 2: $AD=BD=2CD$

Option 3: $AD=2BD=CD$

Option 4: $2AD=BD=CD$

Question : If in a $\triangle ABC$, $\angle ABC=5\angle ACB$ and $\angle BAC=3\angle ACB$, then what is the value of $\angle ABC$?

Option 1: $130°$

Option 2: $80°$

Option 3: $100°$

Option 4: $120°$