The value of m∠ c and m∠ d is 40° , 76°.
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.According to the exterior angle theorem, the exterior angle that results from stretching a triangle's side is equal to the sum of the dimensions of the triangle's two opposed interior angles. The theorem may be used to determine a triangle's unknown angle's measurement. We must first determine the triangle's exterior angle and then its two remote inner angles in order to apply the theorem.
∠ DEF is an exterior angle of the triangle , then
∠ C + ∠ D = ∠ DEF , that is
4y + 7y + 6 = 116
11y + 6 = 116 ( subtract 6 from both sides )
11y = 110 ( divide both sides by 11 )
y = 10
Then
∠ C = 4y = 4(10) = 40°
∠ D = 7y + 6 = 7(10) + 6 = 70 + 6 = 76°
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