Answer:
x = 9 , ∠ QAO = 24°
Step-by-step explanation:
The incentre is where a triangle's three angle bisectors intersect.
An angle bisector is a segment that cuts an angle in half .
the segment OA bisects ∠ QAS , then
∠ SAO = ∠ QAO ( substitute expressions and solve for x )
4x - 12 = 2x + 6 ( subtract 2x from both sides )
2x - 12 = 6 ( add 12 to both sides )
2x = 18 ( divide both sides by 2 )
x = 9
substitute x = 9 into the expression for ∠ QAO
∠ QAO = 2x + 6 = 2(9) + 6 = 18 + 6 = 24°
