Question

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

Explanation:

Step1: Use the triangle - angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((c + 23)+45+6c=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((c+6c)+(23 + 45)=180\), which gives \(7c+68 = 180\).

Step3: Isolate the variable \(c\)

Subtract \(68\) from both sides: \(7c=180 - 68\), so \(7c=112\).

Step4: Solve for \(c\)

Divide both sides by \(7\): \(c=\frac{112}{7}\).

Answer:

\(16\)