Question

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

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, we can write the equation \(45+(3c + 3)+(c+20)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(45+3c + 3+c+20=(3c + c)+(45 + 3+20)=4c+68\). So the equation becomes \(4c+68 = 180\).

Step3: Isolate the variable term

Subtract 68 from both sides of the equation: \(4c+68-68=180 - 68\), which simplifies to \(4c=112\).

Step4: Solve for c

Divide both sides of the equation by 4: \(\frac{4c}{4}=\frac{112}{4}\), so \(c = 28\).

Answer:

28