Answer
$\theta=\beta-\alpha$
Work Step by Step
As we know that the angles $\gamma$ and $\beta$ are supplementary angles therefore
$\gamma+\beta=180^{\circ}$
$\implies \gamma=180^{\circ}-\beta$.......eq(1)
Similarly, we also know that the sum of all three angles of a triangle is $180^{\circ}$
that is $\alpha+\gamma+\theta=180^{\circ}$
Putting value of $\gamma$ from eq(1) in above equation, we obtain:
$\alpha+180^{\circ}-\beta+\theta=180^{\circ}$
This can be rearranged as
$\theta=180^{\circ}-\alpha-180^{\circ}+\beta$
This simplifies to:
$\theta=\beta-\alpha$
