Question

a triangle has interior angle measures of t + 18°, 2t, and 3t − 17°. what is the value of t? write your answer as an integer or as a decimal rounded to the nearest tenth. t = ☐° submit

Explanation:

Step1: Sum of triangle angles is \(180^\circ\)

The sum of the interior angles of a triangle is \(180^\circ\). So we set up the equation: \((t + 18) + 2t + (3t - 17) = 180\).

Step2: Combine like terms

Combine the \(t\) terms and the constant terms: \(t + 2t + 3t + 18 - 17 = 180\), which simplifies to \(6t + 1 = 180\).

Step3: Solve for \(t\)

Subtract 1 from both sides: \(6t = 180 - 1 = 179\). Then divide by 6: \(t=\frac{179}{6}\approx29.8\).

Answer:

\(29.8\)