Question

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

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((a - 35)+(a - 50)+31=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((a + a)+(-35-50 + 31)=180\), which is \(2a-54 = 180\).

Step3: Solve for \(a\)

Add \(54\) to both sides of the equation: \(2a=180 + 54\), so \(2a=234\). Then divide both sides by \(2\): \(a=\frac{234}{2}\).

Answer:

\(117\)