Question

For rhombus LMNO, m∠LON = 102° and NP = 5 units. Use the diagram of rhombus LMNO to find the missing measures. The measure of ∠LPM is °. The measure of ∠PMN is °. The length of LN is units.

Answer 1

LPM = 90

PMN = 51

LN = 10

Answer 2

Answer: angle LPM = 90, angle PMN = 51, side LN = 10

Explanation: Since, In case of rhombus, Diagonals bisect each other with the angle of 90, and corresponding angles are equal.

Here, In rhombus LMNO

$\angle LON=\angle PMN$ = 102° (because both are corresponding angles)

⇒ $\angle PMN =\angle LMN/2$=102°/2

⇒$\angle LPM$ =51°

Now, $\angle LPM$=90°

and, LN=LP+PN=5+5=10 unit.