Lines g and h intersect.

Question

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

Answer 1

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. \( 2x + 26 = 180 \).