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, \(15a + 67+83 = 180\).

Step2: Simplify the left - hand side of the equation

First, add \(67\) and \(83\): \(67 + 83=150\). The equation becomes \(15a+150 = 180\).

Step3: Solve for \(a\)

Subtract \(150\) from both sides: \(15a=180 - 150\). So, \(15a = 30\). Then divide both sides by \(15\): \(a=\frac{30}{15}\).

Answer:

\(a = 2\)