Transversal
cuts parallel lines
and
as shown in the diagram, and m∠4 = 55.1°. What are m∠5 and m∠7?
2 vertical parallel lines. First line passes through points A and B, while second line passes through points C and D. Third line slopes downward through points E and F, intersecting these two lines, forming 8 angles. Fourth angle is 55.1 degrees.
A.
m∠5 = 34.9°, and m∠7 = 145.1°.
B.
m∠5 = 55.1°, and m∠7 = 34.9°.
C.
m∠5 = 124.9°, and m∠7 = 55.1°.
D.
m∠5 = 55.1°, and m∠7 = 124.9°.
E.
m∠5 = 34.9°, and m∠7 = 55.1°.
To determine the measure of angle 5 and angle 7, we need to use the fact that the sum of the interior angles on the same side of the transversal is 180 degrees.
Since angle 4 and angle 5 are on the same side of the transversal and they are adjacent angles, we have:
m∠4 + m∠5 = 180
55.1 + m∠5 = 180
m∠5 = 180 - 55.1
m∠5 = 124.9°
Similarly, since angle 6 and angle 7 are also on the same side of the transversal and adjacent, we have:
m∠6 + m∠7 = 180
m∠7 + 55.1 = 180
m∠7 = 180 - 55.1
m∠7 = 124.9°
Therefore, the correct answer is C.
m∠5 = 124.9°, and m∠7 = 55.1°.
To find the measures of angles 5 and 7, we need to understand the properties of transversals cutting parallel lines.
When a transversal intersects two parallel lines, the corresponding angles (angles that occupy the same relative position at each intersection) are congruent.
In the given diagram, angle 4 is formed by the intersection of the transversal and line AB. Since lines AB and CD are parallel, we can conclude that angle 4 is congruent to angle 5.
Therefore, m∠5 = 55.1°.
Next, we can use the fact that the sum of the measures of the angles around a point is 360 degrees. Angle 7 is formed by the intersection of the transversal and line CD. Since line CD is parallel to line AB, we can conclude that angle 7 is supplementary to angle 5 (they form a straight line together).
So, m∠5 + m∠7 = 180°.
Substituting the value we found for m∠5:
55.1° + m∠7 = 180°
Solving for m∠7:
m∠7 = 180° - 55.1°
m∠7 = 124.9°
Therefore, m∠7 = 124.9°.
In conclusion, m∠5 = 55.1° and m∠7 = 124.9°. The correct answer is option D:
m∠5 = 55.1°, and m∠7 = 124.9°.
To find angles m∠5 and m∠7, we need to understand the properties of transversals cutting parallel lines.
When a transversal cuts two parallel lines, the corresponding angles (angles in the same position relative to the parallel lines) are congruent, and the alternate interior angles (angles on opposite sides of the transversal and between the parallel lines) are also congruent.
In the given diagram, we have two parallel lines and a transversal that intersects them, forming eight angles. We are given that angle m∠4 is 55.1°.
To find angle m∠5, we need to locate its corresponding angle. Angle m∠4 is corresponding to angle m∠5 because both are in the same position relative to the parallel lines. Since angle m∠4 is 55.1°, angle m∠5 must also be 55.1°.
To find angle m∠7, we need to locate its alternate interior angle. Angle m∠4 is an alternate interior angle to angle m∠7 because they are on opposite sides of the transversal and between the parallel lines. Since angle m∠4 is 55.1°, angle m∠7 must also be 55.1°.
Therefore, the values of m∠5 and m∠7 are:
m∠5 = 55.1°
m∠7 = 55.1°
So, the correct answer is option B:
m∠5 = 55.1°, and m∠7 = 34.9°.