Question

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

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). Let the three angles of the triangle be \(76^{\circ}\), \(34^{\circ}\), and \(b\). Then the equation is \(76 + 34 + b=180\).

Step2: Simplify the left - hand side of the equation

First, calculate \(76 + 34\). \(76+34 = 110\). So the equation becomes \(110 + b=180\).

Step3: Solve for \(b\)

Subtract \(110\) from both sides of the equation. \(b=180 - 110\).

Answer:

\(b = 70^{\circ}\)