In order to determine What is The Measure of Angle l in Parallelogram lmno, we must first understand some basic concepts about parallelograms and their properties. A parallelogram is a four-sided figure with two pairs of parallel sides, where opposite sides are congruent and opposite angles are congruent as well. Additionally, the consecutive angles of a parallelogram add up to 180 degrees.
In parallelogram LMNO, we can see that lines LM and NO are parallel and congruent, as are lines LO and MN. Therefore, LMNO is a parallelogram. Furthermore, we know that angle L is congruent to angle N and angle M is congruent to angle O, since they are opposite angles of the parallelogram.
To find the measure of angle M, we need to use some geometry principles and apply them to the given information. One such principle is that the sum of the interior angles of any quadrilateral is 360 degrees. Therefore, we can find the measure of angle M by subtracting the measures of angles L, N, and O from 360 degrees and then dividing the result by 2, since angle M is congruent to angle O.
Let’s begin by finding the measures of angles L and N. Since opposite angles in a parallelogram are congruent, we know that angle L is congruent to angle N. Therefore, we can call their measures “x”. Similarly, we can call the measures of angles M and O “y”, since they are also congruent. Thus, we have:
angle L = angle N = x angle M = angle O = y
Since the consecutive angles of a parallelogram add up to 180 degrees, we know that angles L and M are consecutive angles, as are angles N and O. Therefore, we can write:
angle L + angle M = 180 degrees angle N + angle O = 180 degrees
Substituting in the variables we assigned earlier, we get:
x + y = 180 degrees x + y = 180 degrees
Since we know that lines LM and NO are parallel, we can use the principles of alternate interior angles to find the measure of angle L. Specifically, we know that the measure of angle L is equal to the measure of angle N, since they are alternate interior angles. Therefore, we can write:
angle L = x
Now, we can use the fact that the consecutive angles of a parallelogram add up to 180 degrees to find the measure of angle O. Specifically, we know that the measure of angle O is equal to 180 degrees minus the measure of angle M, since they are consecutive angles. Therefore, we can write:
angle O = 180 degrees – y
Substituting these values into our equation for the sum of the interior angles of the quadrilateral, we get:
x + y + x + (180 degrees – y) = 360 degrees
Simplifying, we get:
2x + 180 degrees = 360 degrees 2x = 180 degrees x = 90 degrees
Now we can use this information to find the measure of angle M, since we know that angle M is congruent to angle O. Specifically, we can substitute our value for x into our equation for the measure of angle O:
angle O = 180 degrees – y 90 degrees = 180 degrees – y y = 90 degrees
Therefore, we have found that the measure of angle M is 90 degrees, or option D in the given answer choices.
To summarize, we found What is The Measure of Angle l in Parallelogram lmno by using the properties of parallelograms and the fact that the consecutive angles of a quadrilateral add up to 360 degrees.
