Look at this diagram:

Question

J
K
L
M
N
O
P
Q

If
KM
and
NP
are parallel lines and mMLJ= 69°, what is mMLO?

Answer 1

To solve for the measure of angle \( mMLO \), we can analyze the given information.

You have two parallel lines \( KM \) and \( NP \), and it is given that the measure of angle \( mMLJ = 69^\circ \).

When dealing with parallel lines, the angles formed with a transversal line (which in this case can be line segment \( MJ \) that intersects both parallel lines) have certain relationships based on the concepts of corresponding angles, alternate interior angles, and consecutive interior angles.

1. Identify the angles:

   • \( mMLJ \) is the angle at point \( M \) that is formed between lines \( MJ \) and \( ML \).
   • The angle \( mMLO \) (which we need to find) is formed at point \( L \) between segments \( ML \) and \( MO \).

2. Angle Relationships: Since \( KM \) and \( NP \) are parallel and \( MJ \) is a transversal, the angle \( mMLJ \) and the angle \( mMLO \) are considered corresponding angles.

3. Corresponding Angles Postulate: According to the corresponding angles postulate, corresponding angles formed by a transversal intersecting two parallel lines are equal. Therefore:

   \[ mMLO = mMLJ \]

4. Substituting the values: Since it is given that \( mMLJ = 69^\circ \):

   \[ mMLO = 69^\circ \]

Thus, the measure of angle \( mMLO \) is \( 69^\circ \).