Point O is the incenter of angle ABC what is measure Qbo

Question

asked Sep 3, 2020 109k views

2 Answers

Igby Largeman · Answer 1 · 2020-09-10T05:04:24+0000

Answer:

$m\angle QOB=75^o$

$m\angle QBO=15^o$

Explanation:

see the attached figure to better understand the problem

step 1

Find the measure of angle ∠QBO

we know that

The incenter of a triangle is the intersection of its interior angle bisectors

so

$m\angle QBO=m\angle OBR$

we have

$m\angle OBR=15^o$ ---> given problem

so

$m\angle QBO=15^o$

step 2

Find the measure of angle ∠QOB

we know that

In the right triangle QOB

$m\angle QOB+m\angle QBO=90^o$ ---> by complementary angles

we have

$m\angle QBO=15^o$

substitute

$m\angle QOB+15^o=90^o$

$m\angle QOB=90^o-15^o$

$m\angle QOB=75^o$