Question

Anyone know the answer to this question?

Answer 1

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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Additional comment

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