9514 1404 393
Answer:
140°
Step-by-step explanation:
The value of the exterior angle (x°) is the sum of the other two angles shown. These are known as "remote interior angles."
x° = 64° +76°
x° = 140°
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<em>Additional comment</em>
This relationship derives from the fact that the exterior angle and the adjacent interior angle have a sum of 180° (they are a linear pair). We also know that the adjacent interior angle and the other two given angles have a sum of 180°.
If we call the unknown interior angle U, these relations are ...
64 + 76 + U = 180 . . . . sum of angles in a triangle
x + U = 180 . . . . . . . . . . sum of angles in a linear pair
Comparing these two equations, we see that ...
64 + 76 = x
