Question

Construct a quadrilateral LMON, when LM =$4$cm, MO = $5$ cm, ON =$6.5$ cm, LN = $5.5$ cm and $\angle LMN={105}^{\circ }$. Then, m $\angle MON$ is

• A. ${95}^o$
• B. ${80}^o$
• C. ${40}^o$
• D. ${50}^o$

Answer 1

The correct option is B ${80}^o$

$\Rightarrow$ Draw a line segment LM = 4cm.

$\Rightarrow$ Construct an angle of 105${}^{\circ }$ at point M.

$\Rightarrow$ Cut off MO = 5cm.

$\Rightarrow$ With L as a center and radius LN = 5.5cm, draw an arc.

$\Rightarrow$ With 0 as a center and radius ON = 6.5cm, draw an arc intersecting the previous arc at point N.

$\Rightarrow$ Join LN an ON.

$\Rightarrow$ Measure $\angle$MON.

$\Rightarrow$ We get $\angle MON={80}^{\circ }$.