Why is the sum of angles in a quadrilateral equal to 360 degrees?

Answer 1

A quadrilateral can be divided with a diagonal into two triangles each with an interior angle sum of #180^@#

It really depends upon how far back you want to go for this proof.

If you accept that the interior angles of a triangle add up to #180^@#

#"Interior angles of "triangle DBC = color(blue)(u+s+t=180^@)#

#"Interior angles of "square ABCD = color(green)(p+q+r)+color(blue)(u+s+t)#
#color(white)("XXXXXXXXXXXXXXXXX")=color(green)(180^@)+color(blue)(180^@)#
#color(white)("XXXXXXXXXXXXXXXXX")=360^@#

If you need to prove that the interior angles of a triangle add up to #180^@#
you can use the rule that the interior angles on the opposite sides of a line crossing two parallel lines are equal.

#color(white)("XXXXXXXXXXXXX")= "Sum of angles in a straight line"#
#color(white)("XXXXXXXXXXXXX")= 180^@#

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Answer 2

The sum of angles in a quadrilateral is equal to 360 degrees because a quadrilateral can be divided into two triangles, each of which has a sum of interior angles equal to 180 degrees. Therefore, the total sum of the interior angles in a quadrilateral is twice that of a triangle, which equals 360 degrees.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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