Find the polynomial for the area.
The area is

 ¹/₂( x² - 10y² + 10xy - xy )

Step-by-step explanation:

From the diagram area of the triangle = ¹/₂ ˣ base ˣ height

where the base = x + 10y and the height = x - y

Therefore putting these into the formula above

Area  =   ¹/₂ [( x + 10y )( x -y )]

         =   ¹/₂( x² - xy + 10xy - 10y²)units²

         = ¹/₂( x² - 10y² + 10xy - xy )

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8