Question

find the measure of \\( \angle hyd \\).

Explanation:

Step1: Identify the relationship between angles

$\angle HYD$ and the $126^{\circ}$ angle are supplementary angles (they form a linear pair).

Step2: Use the supplementary - angle formula

If two angles $\alpha$ and $\beta$ are supplementary, then $\alpha+\beta = 180^{\circ}$. Let $\alpha=\angle HYD$ and $\beta = 126^{\circ}$.
We have the equation $\angle HYD+126^{\circ}=180^{\circ}$.

Step3: Solve for $\angle HYD$

Subtract $126^{\circ}$ from both sides of the equation: $\angle HYD=180^{\circ}-126^{\circ}$.
So, $\angle HYD = 54^{\circ}$.

Answer:

$54^{\circ}$