Asked by Alto Saxophone
If M and N are parallel and angle 1 is 135 degrees, what is the measure of angle 2?
An illustration shows a right inclined transversal passing through two parallel lines labeled upper M and upper N. Four angles are formed at the intersections of the transversal with upper M and upper N. The angles formed around the intersection point of the transversal and upper M are labeled clockwise, starting from the upper left quadrant: 1, 2, 4, and 3. The corresponding angles formed around the intersection point of upper N are labeled clockwise, starting from the upper left quadrant: 5, 6, 8, and 7.$$
An illustration shows a right inclined transversal passing through two parallel lines labeled upper M and upper N. Four angles are formed at the intersections of the transversal with upper M and upper N. The angles formed around the intersection point of the transversal and upper M are labeled clockwise, starting from the upper left quadrant: 1, 2, 4, and 3. The corresponding angles formed around the intersection point of upper N are labeled clockwise, starting from the upper left quadrant: 5, 6, 8, and 7.$$
Answers
Answered by
Alto Saxophone
Just out of curiostity, if I didn't add the An illustration shows a right inclined transversal passing through two parallel lines labeled upper M and upper N paragraph, would the question still be solvable?
Answered by
GPT-4o mini
Given that lines M and N are parallel and that angle 1 measures 135 degrees, we can use the properties of parallel lines and transversals to find the measure of angle 2.
When two parallel lines are intersected by a transversal, several angles are formed. The key relationships to remember are:
1. **Corresponding Angles**: These are equal.
2. **Alternate Interior Angles**: These are also equal.
3. **Consecutive Interior Angles**: These angles are supplementary, meaning they add up to 180 degrees.
In your case:
- Angle 1 is given as 135 degrees.
- Angle 1 and angle 2 are consecutive angles on the same side of the transversal. Therefore, they are supplementary.
To find angle 2, we use the supplementary angle relationship:
\[
\text{Angle 1} + \text{Angle 2} = 180^\circ
\]
Substituting the value of angle 1:
\[
135^\circ + \text{Angle 2} = 180^\circ
\]
Now, we solve for angle 2:
\[
\text{Angle 2} = 180^\circ - 135^\circ = 45^\circ
\]
Thus, the measure of angle 2 is **45 degrees**.
When two parallel lines are intersected by a transversal, several angles are formed. The key relationships to remember are:
1. **Corresponding Angles**: These are equal.
2. **Alternate Interior Angles**: These are also equal.
3. **Consecutive Interior Angles**: These angles are supplementary, meaning they add up to 180 degrees.
In your case:
- Angle 1 is given as 135 degrees.
- Angle 1 and angle 2 are consecutive angles on the same side of the transversal. Therefore, they are supplementary.
To find angle 2, we use the supplementary angle relationship:
\[
\text{Angle 1} + \text{Angle 2} = 180^\circ
\]
Substituting the value of angle 1:
\[
135^\circ + \text{Angle 2} = 180^\circ
\]
Now, we solve for angle 2:
\[
\text{Angle 2} = 180^\circ - 135^\circ = 45^\circ
\]
Thus, the measure of angle 2 is **45 degrees**.