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.

Question

Which equation can be used to find the measure of the Angle
ebc ?

A.(x+26)-x=180

B.x+26+x=90

C.x+26=x

D.2x+26=180

Answer 1

To find the measure of angle \( EBC \), we need to analyze the angles formed by the two intersecting lines \( g \) and \( h \).

Given:

• Angle \( EBC = x \)
• Angle \( DBC = x + 26 \)

At the intersection point \( B \), angles \( EBC \) and \( DBC \) are adjacent angles and together they form a straight line. Therefore, their measures add up to 180 degrees.

This leads us to the equation: \[ x + (x + 26) = 180 \] which simplifies to: \[ 2x + 26 = 180 \]

Thus, the correct equation that can be used to find the measure of angle \( EBC \) is:

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