Respuesta :

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Answer:

63 = x

Step-by-step explanation:

We know that a triangle's angles always add up to 180º. Since Line DC is a 180º line, we can subtract 128 from 180.

180 - 128 = 52º

The angle next to A is 52º.

Then, we add 52 and 65 to get the sum of the two angles.

52 + 65 = 117

Finally, subtract 117 from 180 to get our x.

180 - 117 = 63

x = 63

To check, add all the angle values together and if they equal to 180, your answer is correct.

63 + 52 + 65 = 180. Correct!

Answer:  63

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Explanation:

Through the remote interior angle theorem, adding the remote interior angles x and 65 results in the exterior angle 128. Note how the exterior angle is not adjacent to any of the interior angles (which is where the "remote" portion comes from).

x+65 = 128

x+65-65 = 128-65

x = 63

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A longer method involves finding interior angle BAC using the given exterior angle

angle BAC = 180-(exterior angle DAB)

angle BAC = 180-128

angle BAC = 52

So far, the triangle BAC has two known interior angles 65 and 52. The missing angle x adds onto the previous two getting us 180

x+65+52 = 180

x+117 = 180

x = 180-117

x = 63

We get to the same x value.

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