Question

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

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(15t + 67^{\circ}+53^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side of the equation

First, add \(67^{\circ}\) and \(53^{\circ}\): \(15t+120^{\circ}=180^{\circ}\).

Step3: Solve for \(t\)

Subtract \(120^{\circ}\) from both sides: \(15t = 180^{\circ}-120^{\circ}\), so \(15t=60^{\circ}\). Then divide both sides by \(15\): \(t=\frac{60^{\circ}}{15}\).

Answer:

\(t = 4\)