Answered

At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

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].
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.