Question

finding missing angles
$x = \boxed{75}^\circ$
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find measure of vertical angles
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Explanation:

Step1: Identify straight angle sum

A straight angle equals $180^\circ$. The angles $25^\circ$, $80^\circ$, and $x^\circ$ form a straight angle, so:
$$25 + 80 + x = 180$$

Step2: Calculate sum of known angles

Add the given angles together:
$$25 + 80 = 105$$

Step3: Solve for $x$

Subtract the sum from $180^\circ$:
$$x = 180 - 105$$

Answer:

$x = 65^\circ$