Question

what is the value of t?

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(56+(3t + 13)+(t+19)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(56 + 3t+13+t + 19=(3t+t)+(56 + 13+19)=4t+88\).
The equation becomes \(4t + 88=180\).

Step3: Solve for \(t\)

Subtract 88 from both sides: \(4t=180 - 88\), so \(4t=92\).
Divide both sides by 4: \(t=\frac{92}{4}=23\).

Answer:

\(23\)