Question

find the value of x. x =

Explanation:

Answer:

To find the value of \( x \), we use the fact that the sum of angles around a point is \( 180^\circ \) for a straight line (or \( 360^\circ \) for a full circle, but here we consider the straight line formed by \( EK \) and \( JH \), and the angles on one side of \( GK \)).

Looking at the diagram, the angle \( 58^\circ \) and the two angles of \( (x - 3)^\circ \) are on a straight line, so their sum should be \( 180^\circ \).

So we set up the equation:
\( 58 + (x - 3) + (x - 3) = 180 \)

Simplify the left side:
\( 58 + 2(x - 3) = 180 \)

Subtract \( 58 \) from both sides:
\( 2(x - 3) = 180 - 58 \)
\( 2(x - 3) = 122 \)

Divide both sides by \( 2 \):
\( x - 3 = 61 \)

Add \( 3 \) to both sides:
\( x = 61 + 3 \)
\( x = 64 \)

So the value of \( x \) is \( \boxed{64} \).