Question

Will give you five stars if you can answer this ASAP

Answer 1

Figure refer to attachment

Given :

$\sf OL\perp{ON}$

$\sf m\angle{LOM}=3x-15\degree$

$\sf m\angle{MON}=5x-23\degree$

To find :

$\sf m\angle{MON}$

Solution :

As per given in question that $\sf OL\perp{ON}$ so the sum of $\sf m\angle{LOM}$ and $\sf m\angle{MON}$ equal to 90°

$\implies\sf m\angle{LOM}+m\angle{MON}=90\degree$

$\implies\sf 3x-15+5x-23=90$

$\implies\sf 8x-38=90$

$\implies\sf 8x=90+38$

$\implies\sf 8x=128$

$\implies\sf x=\cancel\frac{128}{8}=16$

Putting the value of x

$\implies\sf m\angle{MON}=5x-23\degree$

$\implies\sf m\angle{MON}=5\times{16}-23$

$\implies\sf m\angle{MON}=57\degree$

$\large{\boxed{\sf{m\angle{MON}=57\degree}}}$

Additional information :

★ Sum of linear pair is equal to 180°

★ If two parallel lines are cut by a transversal , then the -

_ pairs of corresponding angle are equal

_ pairs of alternate angles are equal

_ interior angles on the same side of the transversal are supplementary