Question

In ΔABC, ∠A = 50° and the external bisectors of ∠B and ∠C meet at O as shown in figure. The measure of ∠BOC is

Answer 1

Answer:

17

Step-by-step explanation:

Look at Triangle ABC, The rays meet at line BC and they are both from the interior point A. So this means that AB=AC. This makes ABC a isosceles triangle. Using the isosceles triangle theorem, Angle B and Angle C measure is equal to each other so

$50 + x + x = 180$

$50 + 2x = 180$

$2x = 130$

$x = 65$

This means angle b and C of the triangle ABC measure is 65.

External bisector bisect a figure that it makes the original angle split into half that they are equal to each other.

This means the angle below Angle B and angle C measure is 32.5. We can find the measure of Angle B and C in triangle BOC. This is a isosceles triangle as well so

$32.5 + 65 + x = 180$

$98.5 + x = 180$

$x = 81.5$

Angle C is 81.5 as well so

$81.5 + 81.5 = 163$

Find angle o

$180 - 163 = 17$