Question

the diagram shows a triangle. what is the value of t? t = square^{circ} submit

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((t - 45)+81+(t - 44)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((t+t)+(-45 + 81-44)=180\), which simplifies to \(2t+(81-(45 + 44))=180\), then \(2t+(81 - 89)=180\), and further \(2t-8 = 180\).

Step3: Solve for \(t\)

Add \(8\) to both sides of the equation: \(2t-8 + 8=180 + 8\), so \(2t=188\). Divide both sides by \(2\): \(t=\frac{188}{2}\).

Answer:

\(t = 94\)