Question

Lines
x
x and
y
y are parallel. If
A
=
107
°
A=107° then find the values of
G
G and
E
E . Click Here for Help Video.






G
=
G=
°
° and
E
=
E=
107
°
°

Answer 1

g is wrong

Answer 2

To solve the problem, we need to use the properties of parallel lines and the angles formed when a transversal crosses them.

Given that lines \( x \) and \( y \) are parallel and \( A = 107^\circ \):

1. **Corresponding Angles**: If angle \( A \) is at one intersection of the transversal with line \( x \), the corresponding angle on line \( y \) will also be \( 107^\circ \). Therefore, we have:

\[
E = 107^\circ
\]

2. **Alternate Interior Angles**: If angles \( G \) and \( A \) are alternate interior angles formed by the transversal, then they are equal when the lines are parallel. In this case, angle \( G \) will also be equal to \( 107^\circ \):

\[
G = 107^\circ
\]

Since both angles \( G \) and \( E \) are equal to \( 107^\circ \) due to the parallel lines and the properties of angles formed by a transversal, we conclude:

\[
G = 107^\circ \quad \text{and} \quad E = 107^\circ
\]

Answer 3

I apologize for the confusion. Let's clarify how to find angles \( G \) and \( E \) given that \( A = 107^\circ \) and that lines \( x \) and \( y \) are parallel.

1. **Understanding the Angles**:
- Since \( A = 107^\circ \), if angle \( A \) and angle \( E \) are corresponding angles (meaning they occupy the same relative position at each intersection), then angle \( E \) will also equal \( 107^\circ \):
\[
E = 107^\circ
\]

2. **Finding Angle \( G \)**:
- If angle \( G \) is on the same side of the transversal as angle \( A \), it will be an interior angle. According to the property of interior angles on the same side of the transversal, they are supplementary. Therefore, angles \( A \) and \( G \) will add up to \( 180^\circ \):
\[
G + A = 180^\circ
\]
- Substituting the value of \( A \):
\[
G + 107^\circ = 180^\circ
\]
- Solving for \( G \):
\[
G = 180^\circ - 107^\circ = 73^\circ
\]

So the correct values are:
- \( G = 73^\circ \)
- \( E = 107^\circ \)

If you have more specific details about the relationships of the angles, please provide them, and I'll adjust the explanation accordingly!