Question

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

Explanation:

Step1: Recall the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, for a triangle with angles \(11a\), \(58^{\circ}\), and \(78^{\circ}\), we have the equation \(11a + 58+78=180\).

Step2: Simplify the left - hand side of the equation

First, add \(58\) and \(78\): \(58 + 78=136\). The equation becomes \(11a+136 = 180\).

Step3: Solve for \(11a\)

Subtract \(136\) from both sides of the equation: \(11a=180 - 136\). Then \(180-136 = 44\), so \(11a = 44\).

Step4: Solve for \(a\)

Divide both sides of the equation \(11a = 44\) by \(11\). We get \(a=\frac{44}{11}\).

Answer:

\(a = 4\)