Question

given an equilateral triangle ABC and a point O inside it angle BOC =99°,a nd angle AOC=129° find the largest angle of the triangle with side lengths equal to AO,BO andCO

Answer 1

Refer to the attached image.

Given: An equilateral triangle ABC, with $\angle BOC = 99^\circ$ and $\angle AOC = 129^\circ$.

We have to determine the largest angle of the triangle with side lengths equal to AO, BO and CO. The largest angle of the triangle formed with sides AO, BO and CO is $(\angle AOB + \angle BOC)$.

Since, all the angles at the center forms a circle, so the sum of all the angles is 360 degrees.

Therefore, $\angle AOC + \angle BOC + \angle AOB = 360^\circ$

$129^\circ + 99^\circ + \angle AOB = 360^\circ$

$228^\circ + \angle AOB = 360^\circ$

$\angle AOB = 132^\circ$

Now, the largest angle with sides OA, OB and OC

= $(\angle AOB + \angle BOC)$

= $132^\circ + 99^\circ$

= $231^\circ$

Therefore, the largest angle of triangle with side lengths equal to AO,BO and CO is  $231^\circ$.