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oee [108]
3 years ago
15

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

Mathematics
2 answers:
Rom4ik [11]3 years ago
8 0

105 got it right on edg.

sergij07 [2.7K]3 years ago
5 0

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°

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Hello There!

I believe that the relationships that can help you solve this problem are that the angle is Complementary and Supplementary. It is complementary because within the angle, there is an angle that is 90°. It is also supplementary because the angle itself is 180° making the angle supplementary.

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