Lines m and n are parallel. Angle E measures (3x+18) degrees and angle B measures (14x−8) degrees. What is the value of x?
(1 point)
Since lines m and n are parallel, angle B and angle E are corresponding angles. Corresponding angles are congruent, which means they have the same measure.
Therefore, we can set up the equation:
3x + 18 = 14x - 8
Simplifying this equation, we get:
18 + 8 = 14x - 3x
26 = 11x
Dividing both sides by 11, we find:
x = 26/11
Therefore, the value of x is 26/11 or approximately 2.36.
Line segment AC¯¯¯¯¯¯¯¯ is a perpendicular bisector of segment BD¯¯¯¯¯¯¯¯, with the two segments meeting at point E. What is true of segment BE¯¯¯¯¯¯¯¯? (1 point)
It must be the same length as segment AB¯¯¯¯¯¯¯¯.
It must be the same length as segment BC¯¯¯¯¯¯¯¯.
It must be the same length as segment DE¯¯¯¯¯¯¯¯.
It must be the same length as segment EA¯¯¯¯¯¯¯¯.
The correct answer is "It must be the same length as segment DE¯¯¯¯¯¯¯¯."
Since AC¯¯¯¯¯¯¯¯ is a perpendicular bisector of segment BD¯¯¯¯¯¯¯¯, it means that point E is the midpoint of segment BD¯¯¯¯¯¯¯¯. This implies that segment BE¯¯¯¯¯¯¯¯ is equal in length to segment DE¯¯¯¯¯¯¯¯.
To find the value of x, we can use the fact that when two lines are parallel, the corresponding angles are equal. Therefore, angle E is equal to angle B.
We are given that angle E measures (3x+18) degrees and angle B measures (14x−8) degrees.
Setting up an equation, we have:
3x + 18 = 14x - 8
To solve for x, we can start by isolating the variable terms on one side of the equation and the constant terms on the other side:
18 + 8 = 14x - 3x
26 = 11x
Dividing both sides of the equation by 11:
x = 26/11
Simplifying the fraction, we have:
x = 2.36
Therefore, the value of x is approximately 2.36.