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I don't understand, help.​

I don't understand, help.​-example-1
User Guycole
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1 Answer

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9514 1404 393

Answer:

  • x = 20°
  • y = 70°

Explanation:

The hash marks indicate that the lower triangle is isosceles. That means its base angles are equal. The external angle marked 40° will be the sum of those two equal angles, so ...

x + x = 40°

x = 20°.

x is one of the two acute angles in the right triangle. The other is y, which is the complement of x.

y = 90° -x = 90° -20°

y = 70°

_____

Additional comments

The angle marked 40° is one of a "linear pair". The other angle in that pair is the obtuse angle in the lower triangle. Its measure is 180°-40° = 140°. The two base angles of that isosceles triangle are both x°, so you have ...

x° +x°+140° = 180°

2x° = 180° -140° = 40°

That is, the sum of the two angles will be equal to the external angle marked 40°. The relevant theorem says "an exterior angle is equal to the sum of the remote interior angles." Remembering this is a useful shortcut, so you don't have to find the third interior angle, which is 140° in this case.

User FIXI
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