Question

the diagram shows a triangle. what is the value of t? write your answer as an integer or as a decimal rounded to the nearest tenth. t =

Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((3t - 10)+(9t - 15)+(3t - 11)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((3t+9t + 3t)+(-10-15 - 11)=180\), which gives \(15t-36 = 180\).

Step3: Solve for \(t\)

Add \(36\) to both sides of the equation: \(15t=180 + 36\), so \(15t=216\). Then divide both sides by \(15\): \(t=\frac{216}{15}=14.4\).

Answer:

\(t = 14.4\)