Question

m∠abc = m∠bad because they are alternate interior angles.
m∠bca = m∠cae because they are alternate interior angles.
m∠bad + x° + m∠cae = 180° because the three angles form a straight line.
so the value of x must be

Explanation:

Step1: Identify known angle values

From alternate interior angles:
$m\angle BAD = 52^\circ$, $m\angle CAE = 84^\circ$

Step2: Use straight line angle sum

Substitute into $m\angle BAD + x^\circ + m\angle CAE = 180^\circ$
$52 + x + 84 = 180$

Step3: Calculate $x$

Simplify and solve for $x$:
$x = 180 - 52 - 84$
$x = 44$

Answer:

$44$