Question

the diagram shows a triangle. what is the value of c? c = °

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((c - 40)+(2c - 50)+30=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(c-40 + 2c-50 + 30=(c + 2c)+(-40-50 + 30)=3c-60\).
The equation becomes \(3c-60 = 180\).

Step3: Solve for \(c\)

Add \(60\) to both sides of the equation: \(3c-60+60=180 + 60\), which gives \(3c=240\).
Divide both sides by \(3\): \(c=\frac{240}{3}\).

Answer:

\(c = 80\)