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, \((2t + 17)+(t + 40)+99=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2t+t+17 + 40+99=180\), which gives \(3t+(17 + 40+99)=180\). Then \(3t + 156=180\).

Step3: Solve for \(t\)

Subtract 156 from both sides: \(3t=180 - 156\). So \(3t = 24\). Divide both sides by 3: \(t=\frac{24}{3}\).

Answer:

\(t = 8\)