Question

Point O is the incenter of ΔABC. What is mQBO? mQBO is ___ degrees.

Answer 1

The answer is 12 degrees

Answer 2

Answer:

$m\angle QBO=12$

Step-by-step explanation:

We have been given that point O is the in-center of triangle ABC. We are asked to find the measure of angle QBO.

We know that in-center of a triangle is the point, where three angle bisectors of triangle meet.

Since O is in-center, so AO will be angle bisector. We will find the value of x by equating the expression for angle QAO to angle SAO as:

$2x+6=4x-12$

$2x+6-6=4x-12-6$

$2x=4x-18$

$2x-4x=4x-4x-18$

$-2x=-18$

$\frac{-2x}{-2}=\frac{-18}{-2}$

$x=9$

Now we will substitute $x=9$ in the expression for measure of angle QBO.

$m\angle QBO=3x-15$

$m\angle QBO=3*9-15$

$m\angle QBO=27-15$

$m\angle QBO=12$

Therefore, the measure of angle QBO is 12 degrees.