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sertanlavr [38]
3 years ago
13

What is the value of k?

Mathematics
1 answer:
ale4655 [162]3 years ago
4 0

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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Answer:

4/5

Step-by-step explanation:

3/5+1/5

3+1 /5

simplifies to:

4/5

6 0
3 years ago
Where can the prpendicular bisectors of an acute triangle intersect?
ch4aika [34]
<span>The meeting point of the 3 </span>perpendicular bisectors<span> of a triangle's sides is called </span><span>the circumcenter.
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so the answer is "a"

Source:
http://www.1728.org/trictr.htm
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8 0
4 years ago
Round 2.77247497243 to the nearest millionth.
Tom [10]

Answer:   2.7725

Step-by-step explanation:

8 0
3 years ago
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What's the verbal expression for "4(2x-7)"
Tomtit [17]
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7 0
4 years ago
Fiona has 18 coins, consisting of quarters and dimes, in her pocket. She has 6 more dimes than quarters. How many quarters does
alexandr402 [8]

Answer:

Fiona has 6 quarters

Step-by-step explanation:

If Fiona were to have 1 quarter and 1+6 dimes she would have 8 coins

If she were to have 2 quarters and 2+6 dimes she would have 10 coins

If she were to have 3 quarters and 3+6 dimes she would have 12 coins

If she were to have 4 quarters and 4+6 dimes she would have 14 coins

If she were to have 5 quarters and 5+6 dimes she would have 16 coins

If she were to have 6 quarters and 6+6 dimes she would have 18 coins

Therefore, she has to have 6 quarters in order to have 6 more dimes and a total of 18 coins

I hope this helps, and I'm sorry it took so long for me to write this out

7 0
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