Answer:
m<BXY = 36degrees
Step-by-step explanation:
If XY bisects ∠AXB, then;
<AXY + <BXY = <AXB
Given
m∠AXY = (3x^2 - 12)°
m∠AXB = -18x°
Required
Find m∠BXY.
From the formula above;
Find m∠BXY = <AXB - <AXY
m<BXY = -18x - (3x^2-12)
m<BXY = -18x - 3x^2 + 12
m<BXY = -3x^2 -18x + 12
Also <AXY = m<BXY
3x^2 - 12 = -3x^2 -18x + 12
6x^2 + 18x -24 = 0
x^2+3x-4 = 0
Factorize
x = -3±√9+16/2
x = -3±5/2
x = -3+5/2 and -3-5/2
x = 2/2 and -8/2
x = 1 and -4
Substitute x = 1 into m<BXY
m<BXY = -3x^2 -18x + 12
m<BXY = -3(1)^2 -18(1) + 12
m<BXY = -3 -18+ 12
m<BXY = -9
when x= -4
m<BXY = -3(-4)^2 -18(-4) + 12
m<BXY = -3(16) +72+ 12
m<BXY = -48+84
m<BXY = 36degrees
