Question

find the value of x. 136° 54°

Explanation:

Step1: Find sum of known arcs

$136^\circ + 54^\circ = 190^\circ$

Step2: Find remaining arc measure

The total circumference of a circle is $360^\circ$, so the arc opposite $x$ is:
$360^\circ - 190^\circ = 170^\circ$

Step3: Calculate $x$ using intersecting chords theorem

The measure of an angle formed by two intersecting chords is half the sum of the measures of the intercepted arcs. Here, $x$ is half the sum of arc $FG$ and arc $HJ$:
$x = \frac{136^\circ + 54^\circ}{2}$
$x = \frac{190^\circ}{2}$

Answer:

$95^\circ$