Answer:
x = 8
Explanation:
Find the measure of angle WJZ.
Since angles on a straight line sum to 180°:
⇒ m∠GJH + m∠HJW + m∠WJZ = 180°
⇒ 90° + 18° + m∠WJZ = 180°
⇒ 108° + m∠WJZ = 180°
⇒ 108° + m∠WJZ - 108° = 180° - 108°
⇒ m∠WJZ = 72°
According to the Vertical Angles Theorem, when two straight lines intersect, the opposite vertical angles are congruent.
Since line GJZ and line LJW intersect, then ∠GJL and ∠WJZ are vertical angles and therefore congruent:
⇒ m∠GJL = m∠WJZ
⇒ (9x)° = 72°
⇒ 9x = 72
⇒ 9x ÷ 9 = 72 ÷ 9
⇒ x = 8
Therefore, the value of x is 8.