Question

In an isosceles triangle ABC, AB = AC and angleA = 50° If BO and CO are the bisectors of angle B and
angle C respectively, find angle BOC.​

Answer 1

Answer:

In ABC,

angle B=angle C                       (angle opposit to equal sides)

A+B+C=180

50+2B=180

2B=180-50

B=130/2

B=65

B=C=65

1/2B=1/2C=65/2

=32.5

In BOC

1/2B+1/2C+AOB=180

32.5+32.5+AOB=180

AOB=180-65

AOB=115

Step-by-step explanation:

Answer 2

Answer:

The answer is 82.5°.

Step-by-step explanation:

Since the triangle is isosceles and one angle is 50°,

So let angle ABC and angle ACB be x,

=> x+x+50=180

=> 2x=180-50

=> x=130/2

=> x=65

Now, as BO is the bisector of angle B,

so angle ABO=angle OBC=32.5

Therefore in triangle BOC,

=> 32.5+65+angle BOC=180

=> angle BOC=180-97.5

=> angle BOC=82.5