Line a intersects line b, forming angles of 135 degrees and 45 degrees. A third line,line c, is perpendicular to line a and forms triangle ABC. What is the measure of the angle between lines b and c?
a. 35 degrees
b. 45 degrees
c. 90 degrees
d. 135 degrees
e. Can't be determined
Can you show me how the lines are drawn out?
sorry - no pictures here.
Surely you can draw a reasonable picture of lines a and b.
Let a be the x-axis
Then b is the line y=x (45°)
Now, line c will be parallel to the y-axis.
So, you now have a right triangle with two 45° angles.
To determine the measure of the angle between lines b and c, we need to consider the properties of intersecting lines and perpendicular lines.
First, let's draw the lines based on the given information:
- Line a intersects line b, forming angles of 135 degrees and 45 degrees. We can draw line a cutting across line b, creating angles of 135 degrees and 45 degrees at the point of intersection.
```
b_________
| /
| /
| / a
| /
| /
| /
| /
| /
|_/__________ c
```
- Line c is perpendicular to line a. In a diagram, perpendicular lines are represented by a right angle, which measures 90 degrees. Therefore, we need to draw line c perpendicular to line a.
```
b_________
| /
| /
| / a
| /
| / |
| / |
| / |
| / |
|_/______|_____ c
```
Now, since line c is perpendicular to line a, it is also perpendicular to line b at the point of intersection. Therefore, the angle between line b and line c is also a right angle, measuring 90 degrees.
Hence, the measure of the angle between lines b and c is c. 90 degrees. Therefore, the correct answer is c. 90 degrees.