The value of x equals 24
Explanation:
In order to find the solution to this problem, we know that ∠ABC and ∠DBE are vertical angles because they share the same vertex. Eureka! Vertical angles are always congruent meaning they measure the same value. So, it is true that:
[tex](3x-14)^{\circ}=(2x+10^{\circ}) \\ \\ 3x-14=2x+10 \\ \\ Solving \ for \ x: \\ \\ 3x-2x=14+10 \\ \\ \boxed{x=24}[/tex]
Learn more:
Characteristics of vertical angles: https://brainly.com/question/13410134
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