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3 years ago

14

There are 20 people in a room. If every person shakes hands with every other person, how many handshakes will there be altogethe

r?
Number of handshakes=?

1 answer:

just olya [345]3 years ago

7 0

Answer:400

Step-by-step explanation: if everyone hand shakes every other person the answer will be 400, because 20 times 20 is 400

hope I helped.

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

Mkey [24]

Answer:

$x=14$

$\angle{LMN}=124\textdegree$

Step-by-step explanation:

<u><em>To Determine:</em></u>

Solve for x and find angle LMN.

<u><em>Fetching Information and Solution Steps:</em></u>

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

Learn more about angle bisector and congruent angles from brainly.com/question/711370

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