Question
Lines g and h intersect.
The line g with point D on the left end and point E on the right end and the line h with point A at the top and point C at the bottom intersect at point B Angle E-B-C is x degrees, and angle D-B-C is x + 26 degrees.
Which equation can be used to find the measure of EBC
?
A. (x+26)-x=180
B. x+26+x=90
C. x+26=x
D. 2x+26=180
The line g with point D on the left end and point E on the right end and the line h with point A at the top and point C at the bottom intersect at point B Angle E-B-C is x degrees, and angle D-B-C is x + 26 degrees.
Which equation can be used to find the measure of EBC
?
A. (x+26)-x=180
B. x+26+x=90
C. x+26=x
D. 2x+26=180
Answers
GPT-4o mini
To determine the correct equation for the angles formed by the intersecting lines g and h, we can analyze the situation given the angles described.
You have:
- Angle E-B-C is \( x \) degrees.
- Angle D-B-C is \( x + 26 \) degrees.
Since point B is the intersection of lines g and h, angles E-B-C and D-B-C are adjacent angles that form a linear pair. This means they are supplementary angles, and their measures add up to 180 degrees.
Thus, we can set up the equation:
\[
x + (x + 26) = 180
\]
Simplifying this, we find:
\[
2x + 26 = 180
\]
Therefore, the correct equation that can be used to find the measure of angle EBC is:
**D. \( 2x + 26 = 180 \)**
You have:
- Angle E-B-C is \( x \) degrees.
- Angle D-B-C is \( x + 26 \) degrees.
Since point B is the intersection of lines g and h, angles E-B-C and D-B-C are adjacent angles that form a linear pair. This means they are supplementary angles, and their measures add up to 180 degrees.
Thus, we can set up the equation:
\[
x + (x + 26) = 180
\]
Simplifying this, we find:
\[
2x + 26 = 180
\]
Therefore, the correct equation that can be used to find the measure of angle EBC is:
**D. \( 2x + 26 = 180 \)**