Answer:
x = 6; ∠ONP = 24°
Step-by-step explanation:
1. Find the value of x
[tex]\begin{array}{rcl}\angle MNP & = & \angle MNO + \angle ONP\\3x^{2} + 12 & = & x^{2} + 10x + x^{2} - 2x\\3x^{2} + 12 & = & 2x^{2} + 8x\\x^{2} + 12 & = & 8x\\x^{2} -8x + 12 & = & 0\\(x - 2)(x - 6) & = & 0\\\end{array}[/tex]
[tex]x = 2 \text{ or }x = 6[/tex]
2. Find the measures of the angles
(a) x = 2
∠ONP = x² - 2x = 2² - 2(2) = 4 - 4 = 0
This answer does not make sense because O lies in the interior of ∠MNP.
We disregard x = 2.
(b) x = 6
∠ONP = x² - 2x = 6² - 2(6) = 36 - 12 = 24
