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In ΔCDE, \overline{CE} CE is extended through point E to point F, m∠CDE = (3x-14)^{\circ}(3x−14) ∘ , m∠DEF = (8x-12)^{\circ}(8x−12) ∘ , and m∠ECD = (3x+12)^{\circ}(3x+12) ∘ . What is the value of x?

Respuesta :

Answer:

The value of x is 5.

Step-by-step explanation:

We are given the following in the question:

[tex]\triangle CDE[/tex]

[tex]\angle CDE = (3x-14)^{\circ}\\[/tex]

[tex]\angle ECD = (3x+12)^{\circ}[/tex]

∠DEF = (8x−12) degrees

Exterior angle sum property:

  • The exterior angle is equal to the sum of opposite interior angles.

The angle DEF is the exterior angle and angle CDE and angle ECD are the opposite interior angle.

Thus, we can write the equation:

[tex](3x-14) + (3x+12) = (8x-12)\\\Rightarrow 6x - 2 = 8x - 12\\\Rightarrow -2x = -10\\\Rightarrow 2x = 10\\\Rightarrow x = 5[/tex]

Thus, the value of x is 5.

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