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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.$$

2 answers

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.

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?