Question
If angle, FGE equals 5X +10 find the value of X so that line FC is perpendicular to line AE
Answers
Answered by
GPT-4o mini
To determine the value of \( X \) so that line \( FC \) is perpendicular to line \( AE \), we need to understand the relationship between the angles formed by perpendicular lines.
When two lines are perpendicular, the angles formed at their intersection add up to \( 90^\circ \). Depending on the context of your problem, if we assume that angle \( FGE \) is one of the angles formed where lines \( FC \) and \( AE \) intersect, we can write the following equation:
\[
5X + 10 + 90 = 180
\]
This equation assumes that \( FGE \) forms a right angle with the other angle at the intersection (which is \( 90^\circ \)). However, if \( FGE \) is the angle we want to set to \( 90^\circ \) (i.e., has to be a right angle to make these lines perpendicular), we set:
\[
5X + 10 = 90
\]
Now, let's solve for \( X \):
1. Subtract \( 10 \) from both sides:
\[
5X = 90 - 10
\]
\[
5X = 80
\]
2. Divide by \( 5 \):
\[
X = \frac{80}{5}
\]
\[
X = 16
\]
Thus, the value of \( X \) needed for line \( FC \) to be perpendicular to line \( AE \) is \( X = 16 \).
When two lines are perpendicular, the angles formed at their intersection add up to \( 90^\circ \). Depending on the context of your problem, if we assume that angle \( FGE \) is one of the angles formed where lines \( FC \) and \( AE \) intersect, we can write the following equation:
\[
5X + 10 + 90 = 180
\]
This equation assumes that \( FGE \) forms a right angle with the other angle at the intersection (which is \( 90^\circ \)). However, if \( FGE \) is the angle we want to set to \( 90^\circ \) (i.e., has to be a right angle to make these lines perpendicular), we set:
\[
5X + 10 = 90
\]
Now, let's solve for \( X \):
1. Subtract \( 10 \) from both sides:
\[
5X = 90 - 10
\]
\[
5X = 80
\]
2. Divide by \( 5 \):
\[
X = \frac{80}{5}
\]
\[
X = 16
\]
Thus, the value of \( X \) needed for line \( FC \) to be perpendicular to line \( AE \) is \( X = 16 \).