Stacy drew a triangle to explain the relationship between the angles of a triangle and an exterior angle. She labeled the interior angles 1,

Question

Stacy drew a triangle to explain the relationship between the angles of a triangle and an exterior angle. She labeled the interior angles 1, 2, and 3. She labeled as 4 the exterior angle that is adjacent to angle 2. Triangle with angles labeled 1, 2, 3, & exterior angle at angle 2 is labeled 4. What should Stacy do to explain the relationship between an exterior angle and the interior angles in a triangle?

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Bình An 4 years 2021-09-04T01:34:34+00:00 1 Answers 17 views 0

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  1. Helga
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    2021-09-04T01:35:50+00:00
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    9514 1404 393

    Explanation:

    Stacy can write two equations showing the relationships of the angles:

      ∠1 +∠2 +∠3 = 180° . . . . . . . sum of angles in a triangle

      ∠2 +∠4 = 180° . . . . . . . . . . angles of a linear pair are supplementary

    __

    Subtracting the second equation from the first gives …

      (∠1 +∠2 +∠3) -(∠2 +∠4) = (180°) -(180°)

      ∠1 +∠3 -∠4 = 0

    Adding ∠4 to both sides gives the relationship Stacy is looking for:

      ∠1 +∠3 = ∠4

    _____

    Alternative approach

    Stacy could subtract ∠2 from both equations to give …

      ∠1 +∠3 = 180° -∠2

      ∠4 = 180° -∠2

    Then she could equate the two expressions for 180° -∠2:

      ∠1 +∠3 = ∠4

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )