Rhombus LMNO is shown with its diagonals. Angle MNO measures 112 ° . What is the measure of angle LMN 34 ° 45 ° 56 ° 68 °
Accepted Solution
Answer:The measure of angle LMN is 68° ⇒ the last answerStep-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°
