Question

$mangle efg = mangle feh$ because they are alternate interior angles.$mangle fge = mangle gei$ because they are alternate interior angles.$mangle feh + x^circ + mangle gei = 180^circ$ because the three angles form a straight line.so the value of $x$ must be

Explanation:

Step1: Substitute alternate interior angles

From given, $m\angle FEH = 64^\circ$, $m\angle GEI = 70^\circ$

Step2: Use straight line angle sum

The angles sum to $180^\circ$, so:
$$64^\circ + x^\circ + 70^\circ = 180^\circ$$

Step3: Calculate sum of known angles

$$64 + 70 = 134$$

Step4: Solve for $x$

$$x = 180 - 134$$

Answer:

$46^\circ$