Question

In the triangle ABC, O is the incentre of triangle ABC. $\angle$OAF = 35° and $\angle$OBD = 20°, find the value of $\angle$ACB.

• A. 35°
• B. 120°
• C. 110°
• D. 70°

Answer 1

The correct option is D 70°

Here, we have O as incentre which means CE, AD and BF are angle bisectors.
$\angle$OAF = $\angle$OAE = 35°
So, $\angle$BAC = 35° + 35° = 70°

Similarly,
$\angle$OBD = $\angle$OBE = 20°
So, $\angle$ABC = 20° + 20° = 40°

We know that sum of all interior angles in a triangle is equal to 180°.
So, $\angle$ABC + $\angle$BAC + $\angle$ACB = 180°
$\Rightarrow$ 70° + 40° + $\angle$ACB = 180°
$\Rightarrow$ $\angle$ACB = 180° - 110° = 70°