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3 years ago

Rhombus LMNO is shown with its diagonals.

Mathematics

2 answers:

KatRina [158]3 years ago

7 0

Answer:

Step-by-step explanation:

andrew11 [14]3 years ago

3 0

Answer:

The measure of angle LMN is 68° ⇒ the last answer

Step-by-step explanation:

* Lets revise the properties of the rhombus

- The rhombus has 4 equal sides in length

- Every two opposite angles are equal in measure

- Every two adjacent angles are supplementary (their sum = 180°)

- The two diagonals bisect each other

- The two diagonals perpendicular to each other

- The two diagonals bisect the vertices angles

* Lets solve the problem

∵ LMNO is a rhombus

∴ ∠LMN and ∠MNO are adjacent angles

∴ ∠LMN and ∠MNO are supplementary

∴ m∠LMN + ∠MNO = 180°

∵ m∠MNO = 112°

∴ m∠LMN + 112° = 180° ⇒ subtract 112 from both sides

∴ m∠LMN = 68°

* The measure of angle LMN is 68°

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