In triangle LMN, m∠L = (4c + 47)°. If the exterior angle to ∠L measures 69°, determine the value of c.
c = 36
c = 34
c = 16
c = 11
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To find the value of c, we can use the fact that the exterior angle of a triangle is equal to the sum of its remote interior angles.
In triangle LMN, the exterior angle to ∠L is 69°. The remote interior angles are ∠L and ∠M. Therefore, we have the equation: ∠L + ∠M = 69°.
We are also given that ∠L = (4c + 47)°. Substituting this expression into the equation, we get: (4c + 47)° + ∠M = 69°.
Simplifying the equation, we have: 4c + 47 + ∠M = 69.
Subtracting 47 from both sides of the equation, we get: 4c + ∠M = 22.
Since we don't have enough information about the angles in triangle LMN to solve for ∠M, we cannot determine the value of c.