In ΔABC, D is a point on AC such that AB = BD = DC, if ∠BAD = 70°, then the measure of (∠B + ∠C) is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 110°.
Angles opposite to the equal sides are equal.
The sum of angles of a triangle = 180°
AB = BD = DC
∠BAD = 70°
ΔABD is isosceles triangle.
∠BDA = ∠BAD = 70°
So, ∠ABD = 180° – 70° – 70° = 40°
⇒ ∠BDC = 180° – 70° = 110°
Now ΔBDC is also isosceles triangle,
⇒ ∠DBC = ∠DCB = (180° – 110°)/2 = 35°
⇒ ∠B = 40° + 35° = 75°
⇒ ∠C = 35°
The value of (∠B + ∠C) = 75° + 35° = 110°