1. **State the problem:** We need to find the measure of angle $x$ given that angles $\angle YXZ = 97^\circ$ and $\angle WXY = x^\circ$ are adjacent angles on a straight line.
2. **Formula and rule:** Adjacent angles on a straight line sum to $180^\circ$. This means:
$$x + 97 = 180$$
3. **Solve for $x$:**
$$x = 180 - 97$$
4. **Calculate:**
$$x = 83$$
5. **Answer:** The measure of angle $x$ is $83^\circ$.
Angle Measure 8313Ae
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