Question

solve for the value of t.

Explanation:

Step1: Set up the equation

Since the two angles are supplementary (they form a linear pair), their sum is \(180^{\circ}\). So, \((9t + 3)+(4t-5)=180\).

Step2: Simplify the left - hand side

Combine like terms: \(9t+4t+3 - 5=180\), which simplifies to \(13t-2 = 180\).

Step3: Isolate the term with \(t\)

Add \(2\) to both sides: \(13t-2+2=180 + 2\), so \(13t=182\).

Step4: Solve for \(t\)

Divide both sides by \(13\): \(t=\frac{182}{13}\).

Answer:

\(t = 14\)