use the following information
angle and variable (angle on the left and variable on the right).
exterior angle ,w
interior adjacent angle , x
interior non-adjacent angle 1, y
interior non-adjacent angle 2, z
prove that an exterior angle of triangle is equal to the sum of the non-adjacent interior angles of that triangle?
2016-04-14 11:39 pm
回答 (3)
2016-04-14 11:43 pm
The sum of the angles in a triangle add up to 180°
x + y + z = 180°
The exterior angle and the adjacent interior angle are supplementary (form a straight line) so they also add up to 180°
w + x = 180°
These expressions both equal 180° so equate them.
w + x = x + y + z
Subtract x from both sides:
w = y + z
Therefore the exterior angle is equal to the sum of the non-adjacent interior angles of that triangle.
x + y + z = 180°
The exterior angle and the adjacent interior angle are supplementary (form a straight line) so they also add up to 180°
w + x = 180°
These expressions both equal 180° so equate them.
w + x = x + y + z
Subtract x from both sides:
w = y + z
Therefore the exterior angle is equal to the sum of the non-adjacent interior angles of that triangle.
2016-04-14 11:42 pm
Umm... The angle and the exterior angle are supplementary (they add up to 180 degrees.) The interior angles add up to 180 degrees.... so....
w + x = 180
x + y + z = 180
==> w = y+z
w + x = 180
x + y + z = 180
==> w = y+z
2016-04-14 11:39 pm
收錄日期: 2021-05-03 07:20:35
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