Question

Find m/KMN. L 60° K 1⁰40 6x (11x+15)° N​

Answer 1

Answer:

the answer is angle 90

Step-by-step explanation:

Answer 2

Answer:

  114°

Step-by-step explanation:

The exterior angle is the sum of the remote interior angles.

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setup

  (11x +15)° = 60° +6x°

solution

  5x = 45 . . . . . . . . . divide by °, subtract 15+6x

  x = 9 . . . . . . . . . . divide by 5

The measure of exterior angle KMN is ...

  m∠KMN = (11(9) +15)° = 114°

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Additional comment

Both the sum of interior angles and the sum of angles of a linear pair are 180°. If M represents the interior angle at vertex M, then we have ...

  60° +6x° +M = 180°

  (11x +15)° +M = 180°

Equating these expressions for 180° and subtracting M gives the relation we used above:

  (11x +15)° +M = 60° +6x° +M . . . . . equate the two expressions for 180°

  (11x +15)° = 60° +6x° . . . . . . . . . . . subtract M

This is also described by "supplements to the same angle are equal."