A straight line is 180°.
The sum of all the angles in a triangle is also 180°.
Let the missing angle be x°.
For the straight line:
x + 2x²+ 3x+ 6 = 180
x = 180 - (2x² + 3x + 6)
x = 180 - 2x² - 3x - 6
x = 174 - 2x² - 3x
For the missing angle in the triangle:
(174 - 2x² - 3x) + 8x + 3x² - 6x = 180
174 - 2x² - 3x + 8x + 3x² - 6x = 180
174 + x² - x = 180
x² - x + 174 - 180 = 0
x² - x - 6 = 0
(x + 2)(x - 3) = 0
x + 2 = 0 or x - 3 = 0
x = -2 or x = 3
The answer is x = -2 or x = 3
Step-by-step explanation:
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