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, \(92^{\circ}+58^{\circ}+(a - 38^{\circ})=180^{\circ}\).

Step2: Simplify the left - hand side of the equation

First, add \(92^{\circ}\) and \(58^{\circ}\): \(92 + 58=150\). The equation becomes \(150^{\circ}+(a - 38^{\circ})=180^{\circ}\). Then, using the associative property of addition \((150 - 38)^{\circ}+a=180^{\circ}\), so \(112^{\circ}+a=180^{\circ}\).

Step3: Solve for \(a\)

Subtract \(112^{\circ}\) from both sides of the equation: \(a=180^{\circ}-112^{\circ}\).

Answer:

\(68\)