The problem asks us to find the value of $t$. The figure shows two adjacent angles, $(9t+3)^\circ$ and $(4t-5)^\circ$, which form a straight line. Therefore, their sum is $180^\circ$.

1. Problem Description

The problem asks us to find the value of $t$. The figure shows two adjacent angles, $(9t+3)^\circ$ and $(4t-5)^\circ$, which form a straight line. Therefore, their sum is $180^\circ$.

2. Solution Steps

Since the two angles form a straight line, their sum must be $180^\circ$. Thus, we have the equation:

$(9t+3) + (4t-5) = 180$

Combining like terms, we get:

$13t - 2 = 180$

Adding 2 to both sides:

$13t = 182$

Dividing both sides by 13:

$t = \frac{182}{13}$

$t = 14$

3. Final Answer

The value of $t$ is 14.