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What is the value of k?

What Is The Value Of K class=

Sagot :

Sqdancefanidn

9514 1404 393

Answer:

  k = 10

Step-by-step explanation:

The useful shortcut* here is that the external angle is equal to the sum of the remote internal angles.

  115° = (4k+5)° +(6k+10)°

  100° = 10k° . . . . . . collect terms, subtract 15°

  k = 10 . . . . . . . . . . divide by 10°

_____

* I call it a shortcut because you can get there from the relations ...

  • the sum of angles in a triangle is 180°
  • a linear pair has a sum of 180°

If we call the internal angles X, Y, and Z, then we have ...

  X + Y + Z = 180° . . .  triangle sum relation

  Y + 115° = 180° . . . . . linear pair relation

Equating the expressions for 180° gives ...

  X + Y + Z = Y + 115°

  X + Z = 115° . . . . . . . . . subtract Y from both sides

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