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It is given that [tex]$\angle ABE$[/tex] and [tex]$\angle DBC$[/tex] are vertical angles. By the Vertical Angles Theorem, [tex]$\angle ABE$[/tex] is congruent to [tex]$\angle DBC$[/tex]. By the definition of congruence, the measure of [tex]$\angle ABE$[/tex] must equal the measure of [tex]$\angle DBC$[/tex]. Then, by the substitution property of equality, [tex]$2x + 6 = x + 10$[/tex]. Applying the subtraction property of equality gives [tex]$x = 4$[/tex].



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It is given that [tex]$\angle ABE$[/tex] and [tex]$\angle DBC$[/tex] are vertical angles. By the vertical angles theorem, [tex]$\angle ABE$[/tex] is congruent to [tex]$\angle DBC$[/tex]. By the definition of congruence, the measure of [tex]$\angle ABE$[/tex] must equal the measure of [tex]$\angle DBC$[/tex]. Then, by the substitution property of equality, we can set up the equation [tex]$2x + 6 = x + 10$[/tex]. Applying the subtraction property of equality gives [tex]$x = 4$[/tex]. Hence, we have proven that [tex]$x = 4$[/tex].

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