Find the measures of all angles formed by line a parallel to line b with transversal m, if:
one angle is 25° bigger than another
To find the measures of all angles formed by line a parallel to line b with transversal m, we first need to understand the concept of parallel lines and transversals.
Parallel lines are lines in a plane that never intersect. In this case, line a is parallel to line b.
A transversal is a line that intersects two or more parallel lines. In this case, transversal m intersects line a and line b.
When a transversal intersects two parallel lines, several pairs of angles are formed, which can be classified based on their positions relative to the parallel lines. These pairs of angles are called corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles.
Now, let's focus on the angles formed by line a parallel to line b with transversal m. Since one angle is 25° bigger than another, let's denote the measure of one angle as x°. The other angle can be represented as (x + 25)°.
Now, based on the relationship between the angles formed by parallel lines and a transversal, we can conclude that:
1. Corresponding angles are congruent - If we have one angle with measure x°, there will be another corresponding angle formed on the other side of the transversal, also measuring x°.
2. Alternate interior angles are congruent - In this case, one angle measures x°, but the other angle is 25° bigger, so it would measure (x + 25)°.
Therefore, the measures of all angles formed by line a parallel to line b with transversal m would be:
- One angle measures x°.
- The corresponding angle on the opposite side of the transversal would also measure x°.
- Another angle measures (x + 25)°.
In summary, we need the value of x to determine the exact measures of the angles.
x+x+25=180
2x+25=180
2x=180-25
2x=155
x=77.5
x=77.5, add 25 and you get the second number
Answer= 77.5, 102.5
all the angles are either congruent or supplementary.
So, if one angle is x, and the other angle is x+25, then
x + x+25 = 180
and now you can finish it off.