Question

the diagram shows a triangle. 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, \(18c + 7=(17c - 4)+72\).

Step2: Simplify the equation

First, expand the right - hand side: \(18c + 7=17c-4 + 72\). Then, simplify the right - hand side further: \(18c + 7=17c + 68\).

Step3: Solve for \(c\)

Subtract \(17c\) from both sides of the equation: \(18c-17c+7=17c-17c + 68\), which gives \(c+7 = 68\). Then subtract \(7\) from both sides: \(c+7-7=68 - 7\).

Answer:

\(c = 61\)