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Convert the flow chart proof into a paragraph proof.

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]. If we let the measure of [tex]$\angle ABE$[/tex] be [tex]$2x + 6$[/tex] and the measure of [tex]$\angle DBC$[/tex] be [tex]$x + 10$[/tex], then by the substitution property of equality, we have [tex]$2x + 6 = x + 10$[/tex]. Applying the subtraction property of equality, we subtract [tex]$x$[/tex] from both sides to get [tex]$x + 6 = 10$[/tex]. Finally, subtracting [tex]$6$[/tex] from both sides, we obtain that [tex]$x = 4$[/tex].

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