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In triangle CDE, angle C = (4x - 16) degrees, angle D = (6x - 1) degrees, and angle E = (4x - 13) degrees. Find angle C.

 Sep 2, 2021
 #1
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Hint:       C+D+E = 180

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

angle C = 44 degrees laugh

 Sep 2, 2021
edited by Guest  Sep 2, 2021
 #2
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Not sure why you would go through the effort of pressing enter so many times, but I might as well put a full walkthrough here.

The guest is correct, the critical information here is that C + D + E = 180, along with the relations.

So, let's expand it through substitution.

 

4x - 16 + 6x - 1 + 4x - 13 = 180

We can also group the terms using the commutative property, making this a lot easier to look at: 

 

14x - 30 = 180

 

Now, we solve a single-variable equation.

 

14x = 210

7x = 105

x = 15

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Now, let's plug this value of x back into the equation for angle C.

 

C = 4x - 16
C = 4*15 - 16

C = 60 - 16
C = 44

 

Thus, angle C has a measure of 44 degrees.

 

And guest, I like the fact that you didn't give the answer right away but instead gave a hint to solve the problem, that's better than a number of other guest posts I've seen on here as answers :D

helperid1839321  Sep 2, 2021

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