In the figure, the horizontal lines are parallel and AB = BC = CD. Find the measure of JM. The diagram is not drawn to scale.
Four horizontal, parallel lines are cut by two transversals. From top to bottom, the transversal on the left intersects the horizontal lines at points M, L, K, and J. From top to bottom, the transversal on the right intersects the horizontal lines at points A, B, C, and D. Line segment M L has a length of 7.
(1 point)
Responses
14
14
21
21
28
28
7
To find the measure of JM, we need to determine the value of M L and M J.
Given that ML = 7 and AB = BC = CD, we can determine the value of AB. Since AB = BC, and BC = CD, AB = CD.
Therefore, AB + BC + CD = 7.
Since AB = CD, we can rewrite this equation as AB + AB + AB = 7.
This simplifies to 3AB = 7.
Dividing both sides by 3, we find that AB = 7/3.
Since MJ and AB are corresponding segments, they are congruent.
Therefore, MJ = AB = 7/3.
So, the measure of JM is 7/3 or 2 1/3.
The correct answer is 7.
To find the measure of JM, we need to use the properties of parallel lines and transversals.
Since the horizontal lines are parallel, the corresponding angles formed by the transversals are congruent.
Let's label the angles formed by the transversal on the left as ∠M, ∠L, ∠K, and ∠J, and the angles formed by the transversal on the right as ∠A, ∠B, ∠C, and ∠D.
Since AB = BC = CD, we know that ∠A = ∠B = ∠C.
Therefore, ∠J = ∠A.
Now, since the angles formed by the transversal on the left are congruent, we have:
∠J + ∠K + ∠L = 180°.
Substituting ∠J = ∠A, we have:
∠A + ∠K + ∠L = 180°.
From the given information, we know that ∠L = 7°.
Substituting this value, we have:
∠A + ∠K + 7° = 180°.
Rearranging the equation, we have:
∠A + ∠K = 180° - 7°.
∠A + ∠K = 173°.
Since ∠A = ∠J, we also know that:
∠J + ∠K = 173°.
Therefore, the measure of JM (∠J) is 173°.
To find the measure of JM, we need to use the information given in the figure.
The figure shows that AB = BC = CD, which means that the line segment BL is equal to the line segment CK, and the line segment AK is equal to the line segment DJ.
We also know that ML has a length of 7.
Since AB = BC = CD, we can divide ML into four equal parts, each with a length of 7/4.
So, each of the line segments BL, CK, and AK has a length of 7/4.
Therefore, the length of JM is equal to the length of ML minus the length of BL, which is 7 - (7/4) = 28/4 - 7/4 = 21/4.
Therefore, the measure of JM is 21/4.