please help me, I don't know how to do this question.
In the illustration (in the link below), suppose l ∥ m and ∠1 = 55°. What are the measures of the other angles?
www.webassign.net/ewenmath10/12-1-013.gif
∠2 = °
∠3 = °
∠4 = °
since you have two parallel lines and a transversal, all the angles are either congruent or supplementary, in pairs.
can someone help me!
To determine the measures of the other angles in the given illustration, you need to consider the relationships between angles formed by parallel lines and transversals.
In the given scenario, we are provided the information that line l is parallel to line m, denoted by l ∥ m. Additionally, we are told that ∠1 has a measure of 55°.
To find the other angle measures, make use of the following angle relationships:
1. Corresponding angles: When a transversal intersects two parallel lines, the corresponding angles formed are congruent.
2. Alternate interior angles: When a transversal intersects two parallel lines, the alternate interior angles formed are congruent.
Now let's analyze the illustration using these angle relationships:
- Based on the parallel lines l and m, we can observe that ∠1 and ∠2 are corresponding angles. Since ∠1 measures 55°, ∠2 will have the same measure.
Therefore, ∠2 = 55°.
- Similarly, ∠1 and ∠3 are alternate interior angles formed by lines l and m. These angles will also have the same measure.
Thus, ∠3 = 55°.
- Finally, ∠4 is an exterior angle formed by the transversals and the parallel lines. It is supplementary to ∠3, which means the sum of their measures is 180°.
Therefore, ∠3 + ∠4 = 180°.
Substituting the known value of ∠3 (55°) into the equation above, we can solve for ∠4:
55° + ∠4 = 180°
∠4 = 180° - 55°
∠4 = 125°.
In summary, based on the given information, we can determine the measures of the other angles as follows:
- ∠2 = 55°
- ∠3 = 55°
- ∠4 = 125°