Question

In ∆ABC,

AD

is the angle bisector of ∠A and

BE

is the angle bisector of ∠B. If

AD

intersects

BE

at point O, find the measure of ∠AOB if:

c

m∠A +m∠B = 110°

Answer 1

We are give the fact that

`m < a + m < b = 110 \: so \\ (1)/(2)m < a + (1)/(2)m < b = 55`
By the definition of an angle bisector

`m < oab = (1)/(2) m < obd = (1)/(2) m < b`
Triangle AOB has measure 180 because it is a triangle,
and
the measure of triangle aob = 180 = (m < oab + m < obd) + m < aob = 55 + m < aob so the measure of angle aob = 125