Question

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

Answer 1

Refer to the attached image.

Given: An equilateral triangle ABC with angle BOC =99°  and angle AOC=129°

To find : The largest angle of the triangle with sides lengths equal to AO,BO and CO

Solution:

Since the angles around the center add up to 360 degrees.

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

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

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

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

$\angle AOB = 132^\circ$

Now, the largest angle with sides lengths equal to AO,BO and CO

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

= $231^\circ$.

Hence, the measure of largest angle with sides OA, OB, OC is $231^\circ$.