Question

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

Explanation:

Step1: Use the triangle - angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((w + 5)+(w - 7)+76=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((w+w)+(5 - 7+76)=180\), which simplifies to \(2w+( - 2 + 76)=180\), and further to \(2w + 74=180\).

Step3: Solve for \(w\)

Subtract \(74\) from both sides: \(2w=180 - 74\), so \(2w = 106\). Then divide both sides by \(2\): \(w=\frac{106}{2}\).

Answer:

\(w = 53\)