Question

If quadrilateral LMNO is a parallelogram, what must the measure of angle LMN be?

Answer 1

Answer:

∠LMN = 105°

Step-by-step explanation:

Quadrilateral LMNO is a parallelogram in which ∠L = 25x° and ∠MNO = (22x + 9)°

We have get the measurement of ∠LMN

Since in a parallelogram opposite angles are equal.

Therefore 25x = 22x + 9

25x - 22x = 9

3x = 9

x = 3

From another property of a parallelogram we know that consecutive angles are supplementary.

∠LMN + ∠ONM = 180°

∠LMN = 180 - ∠OLM = 180 - (25x) = 180 - (25×3)

∠LMN = 180 - 75 = 105°

Answer is ∠LMN = 105°

Answer 2

In the quadrilateral LMNO which is a parallelogram, measure of angle LMN is 105 degrees.

What is parallelogram?

Parallelogram is a closed shaped quadrilateral polygon in which opposite sides is equal and parallel and opposite angles are equal.

Here, Quadrilateral LMNO is a parallelogram, the measure of angle MLO is 25x degrees and the measure of angle MNO is 22x+9 degrees.

As the opposite angle of the parallelogram is equal thus,

$25x=22x+9\\25x-22x=9\\3x=9\\x=3$

Thus the angle MLO is,

$\angle MLO=25\times 3\\\angle MLO=75^o$

As the angle MLO is opposite angle of angle MNO. Thus the measure of the angle MNO is also 75 degrees.

Now the sum of all the interior angles of quadrilateral is equal to 360 degrees. Thus,

$\angle MLO+\angle LMN+\angle MNO+\angle NOL=360\\75+\angle LMN+75+\angle NOL=360\\\angle LMN+\angle NOL=360-150\\\angle LMN+\angle NOL=210^o$

As the opposite angle of the parallelogram is equal. Thus, angle LMN is equal to the angle NOL. Therefore,

$\angle LMN+\angle LMN=210\\2\angle LMN=210\\\angle LMN=105^o$

Thus in the quadrilateral LMNO which is a parallelogram, measure of angle LMN is 105 degrees.

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