What is the length of MN

As here Angle M(63°) is equal to angle N(63°) that means triangle is isosceles triangle which has its two sides equal to each other. in our case ML = MN

so

3x = x +8

2x= 8

x= 8/2 = 4
so length of MN = x + 8 = 4+8 = 12
so ans is option B

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akposevictor akposevictor · Answer 2 · 2021-10-01T15:02:47+02:00

The length of MN is: B. 12

Recall the properties of an isosceles triangle:

An isosceles triangle has two equal base angles.

The two sides opposite each of the base angles are congruent or equal in length.

Thus:

[tex]\triangle LMN[/tex] is an isosceles triangle having two equal base angles. Therefore, the two sides, LM and MN would be equal.

[tex]LM = 3x\\\\MN = x + 8[/tex]

Therefore:

[tex]LM = MN[/tex]

Substitute:

[tex]3x = x + 8[/tex]

Subtract x from both sides

[tex]3x - x = 8\\\\2x = 8[/tex]

Divide both sides by 2

[tex]x = \frac{8}{2}\\\\x = 4[/tex]

Find MN

[tex]MN = 3x[/tex]

Plug in the value of x

[tex]MN = 3(4)\\\\MN = 12[/tex]

The length of MN is: B. 12.

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