Question

MO bisects angle LMN , angle LMO = 6x-22 and angle NMO = 2x +34. Solve for x and find angle LMN.

Answer 1

Answer:

• $x=14$

• $\angle{LMN}=124\textdegree$

Step-by-step explanation:

To Determine:

Solve for x and find angle LMN.

Fetching Information and Solution Steps:

Considering the angle $\angle{LMN}$

As MO bisects the angle $\angle{LMN}$ into two equal angle parts. These equal angles are:

$\angle{LMO}=6x-22$

$\angle{NMO}=2x+34$

As these angles are equal. i.e.

$\angle{LMO}=\angle{NMO}$

$6x-22=2x+34$

$\mathrm{Add\:}22\mathrm{\:to\:both\:sides}$

$6x-22+22=2x+34+22$

$6x=2x+56$

$\mathrm{Subtract\:}2x\mathrm{\:from\:both\:sides}$

$6x-2x=2x+56-2x$

$4x=56$

$\mathrm{Divide\:both\:sides\:by\:}4$

$\frac{4x}{4}=\frac{56}{4}$

$\mathrm{Simplify}$

$x=14$

Hence, $x=14$

As  $\angle{LMN}$ was cut into two equal parts $\angle{LMO}$ and $\angle{NMO}$

So,

$\angle{LMN}$ = $\angle{LMO} + \angle{NMO}$

            = $6x-22+2x+34$

            = $8x + 12$

            = $8(14) + 12$     ∵ $x=14$

            = $124\textdegree$

Therefore, $\angle{LMN}=124\textdegree$

Keywords: angle bisector, congruent angles

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