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15 May, 07:12

Rhombus LMNO is shown with its diagonals.

Angle MNO measures 112°. What is the measure of angle LMN?

34°

45°

56°

68°

+2
Answers (1)
  1. 15 May, 07:31
    0
    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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