Question

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

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(2t + 6t+44^{\circ}=180^{\circ}\).

Step2: Combine like terms

Combine the terms with \(t\): \((2 + 6)t+44^{\circ}=180^{\circ}\), which simplifies to \(8t+44^{\circ}=180^{\circ}\).

Step3: Isolate the term with \(t\)

Subtract \(44^{\circ}\) from both sides: \(8t=180^{\circ}- 44^{\circ}\). So, \(8t = 136^{\circ}\).

Step4: Solve for \(t\)

Divide both sides by \(8\): \(t=\frac{136^{\circ}}{8}\).

Answer:

\(t = 17\)