What is the sum of the measures of the angles of a trapezoid?

Answer 1

The sum of the interior angles of a trapezoid is #360^@#.

There's a general theorem that holds for each quadrilateral: the sum of interior angles of a convex quadrilateral is #360^@#. This can be generalized further to non-convex quadrilaterals. Since trapezoids are convex quadrilaterals, we prove the theorem using the convex assumption.

The proof is quite easy: let's choose a vertex of the convex quadrilateral and connect it to the opposite vertex. We divided the quadrilateral into two triangles and we are left with the following situation:

So the sum of the interior angles of the two triangles equals the sum of the interior angles of the quadrilateral. Since the sum of the interior angles of a triangle is always #180^@#, the sum of the interior angles of two triangles is #360^@# and this ends the proof.

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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.