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
?
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
?
A.(x+26)-x=180
B.x+26+x=90
C.x+26=x
D.2x+26=180
Answers
GPT-4o mini
To find the relationship between the angles formed by the intersecting lines g and h at point B, we can analyze the angles given:
1. Angle E-B-C is \( x \) degrees.
2. Angle D-B-C is \( x + 26 \) degrees.
Since lines g and h intersect, the angles E-B-C and D-B-C are adjacent angles that form a straight line. Therefore, the sum of these angles must be equal to 180 degrees.
We can set up the equation:
\[
x + (x + 26) = 180
\]
This simplifies to:
\[
2x + 26 = 180
\]
Thus, the correct equation to find the measure of \( x \) is:
**D. \( 2x + 26 = 180 \)**.
1. Angle E-B-C is \( x \) degrees.
2. Angle D-B-C is \( x + 26 \) degrees.
Since lines g and h intersect, the angles E-B-C and D-B-C are adjacent angles that form a straight line. Therefore, the sum of these angles must be equal to 180 degrees.
We can set up the equation:
\[
x + (x + 26) = 180
\]
This simplifies to:
\[
2x + 26 = 180
\]
Thus, the correct equation to find the measure of \( x \) is:
**D. \( 2x + 26 = 180 \)**.