Question

the diagram shows a triangle.
what is the value of a?
a = \square^\circ

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(89^\circ + 52^\circ + 3a = 180^\circ\).

Step2: Simplify the left side

Calculate \(89 + 52 = 141\). So, \(141 + 3a = 180\).

Step3: Solve for \(3a\)

Subtract 141 from both sides: \(3a = 180 - 141 = 39\).

Step4: Solve for \(a\)

Divide both sides by 3: \(a = \frac{39}{3} = 13\).

Answer:

\(13\)