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
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Correct Answer: 15 and 125
Solution :
Given: $\angle A=70^{\circ},\angle B=80^{\circ}$, $\angle ACB = 2x^{\circ},$ and $\angle BDC = y^{\circ}$
$\angle C = 180^{\circ}-70^{\circ}-80^{\circ}=30^{\circ}$
$\therefore \angle ACB = 2x^{\circ} = 30^{\circ}$
$⇒x=15^{\circ}$
Now, $\angle BDC=90^{\circ}+\frac{1}{2}\angle A^{\circ}$
⇒ $y=90^{\circ}+\frac{1}{2}\angle 70^{\circ}$
$\therefore y=125^{\circ}$
Hence, the correct answer is 15 and 125.
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