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Given: [tex]\(\angle ABE\)[/tex] and [tex]\(\angle DBC\)[/tex] are vertical angles.

Prove: [tex]\(x=4\)[/tex]

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]. Therefore, we have:

[tex]\[ m \angle ABE = m \angle DBC \][/tex]

Substituting the given expressions, we get:

[tex]\[ 2x + 6 = x + 10 \][/tex]

Applying the subtraction property of equality:

[tex]\[ 2x + 6 - x = x + 10 - x \][/tex]

Simplifies to:

[tex]\[ x + 6 = 10 \][/tex]

Subtracting 6 from both sides, we get:

[tex]\[ x = 4 \][/tex]

Thus, we have proved that [tex]\(x=4\)[/tex].

Sagot :

GinnyAnswer
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]. Therefore, [tex]\(2x + 6 = x + 10\)[/tex].

Next, using the subtraction property of equality, we subtract [tex]\(x\)[/tex] from both sides of the equation:
[tex]\[ 2x + 6 = x + 10 \][/tex]
[tex]\[ 2x + 6 - x = x + 10 - x \][/tex]
This simplifies to:
[tex]\[ x + 6 = 10 \][/tex]

Again, using the subtraction property of equality, we subtract 6 from both sides of the equation:
[tex]\[ x + 6 - 6 = 10 - 6 \][/tex]
This simplifies to:
[tex]\[ x = 4 \][/tex]

Therefore, we have proven that [tex]\(x = 4\)[/tex].
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