Question

what is the value of c? c =

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(3c=(2c - 27)+(2c - 3)\).

Step2: Simplify the right - hand side of the equation

First, combine like terms on the right - hand side: \((2c - 27)+(2c - 3)=2c+2c-27 - 3=4c-30\). So the equation becomes \(3c = 4c-30\).

Step3: Solve for \(c\)

Subtract \(3c\) from both sides of the equation: \(3c-3c=4c - 30-3c\). This gives \(0=c - 30\). Then add 30 to both sides: \(c=30\).

Answer:

\(30\)