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?

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

the range is 19

step-by-step explanation:

the range is biggest number minus the smallest, so in this case it would be

41 - 22 = 19