What is the value of y when line m is parallel to line n?
Lines m and n are parallel. From left to right, line m has points A and B on it. From left to right, line n has points C, D, and F on it. There is a segment connecting points A and F. There is another segment connecting points B and D. Segment A F and segment B D intersect at point E. The measure of angle A B D is 30 degrees. The measure of angle B E F is 110 degrees. The measure of angle C D B is y degrees.
Line m is above line n.
The points upper A and upper B lie on line m. Upper A is to the left of upper B.
The points upper D and upper F lie on the line n. Upper D is to the left of upper F.
The segments upper A upper F and upper B upper D are drawn and intersect in the interior of lines m and n at point upper E forming two triangles.
The point upper C lies on line n to the left of upper D.
Angle upper A upper B upper E is labeled 30 degrees.
Angle upper E upper D upper C is labeled y degrees.
Angle upper B upper E upper F is labeled 110 degrees.
(1 point)
Responses
70
70
110
110
140
140
150
There is not enough information given to determine the value of y.
To find the value of y, we need to use the fact that when two parallel lines are intersected by a transversal, the corresponding angles are equal. In this case, angle ABD is 30 degrees, which means angle BED is also 30 degrees.
Since angle BEF is 110 degrees, angle CED (which is vertically opposite to angle BED) is also 110 degrees.
Now, since the sum of the angles in a triangle is 180 degrees, we can find y by subtracting the measures of angles BED and CED from 180:
y = 180 - 30 - 110 = 40 degrees.
Therefore, the value of y is 40 degrees.
To find the value of y, we can use the property that when two lines are parallel and a transversal cuts through them, the corresponding angles are congruent. In this case, angle BEF and angle CDB are corresponding angles.
We are given that angle BEF measures 110 degrees. Therefore, angle CDB also measures 110 degrees.
So, the value of y is 110 degrees.