AboutJosh Expertise When I work through problems, I like to emphasize concepts which I believe are worth noting. I will try to answer questions in the following areas, but not at the advanced level. Algebra. Sequences & Series. Trigonometry. Functions & Graphs. Coordinate Geometry. Quadratic Polynomials. Exponential & Logarithms. Basic Calculus. Probability, Permutation and Combination. Mathematical Induction. Complex numbers. Physics problems.
Experience I have worked as a teaching assistant in college. My hope is that more people will share knowledge without boundary, give help without seeking recognition or monetary rewards.
Education/Credentials Bachelor degree in Engineering Science
Question hi, i am confused on this question, very simple though: the sum of the interior angles of a convex quadrilateral is 180 or 360 degrees?
Answer Hi Hannah,
You may have learnt that the sum of the interior angles in a triangle add up to 180.
e.g., A
.
.
B-----------------------C
^ABC+^BCA+^CAB=180 degrees
Here, the theorem states that the (four) interior angles of a convex quadrilateral add up to 360 degrees. ......[#1]
A convex quadrilateral is a four-sided polygon, that when you draw a line to join two arbitrary points on its boundary (for instance, consider linking point E and C in the following diagram), the line always cut through the filled area of the quadrilateral (formed by ABCD).
e.g.1, Example of a convex quadrilateral (ABCD)
A--------E-------------B
.
.
.
.
....D
.
------------------C
e.g.2, The following is a non-convex quadrilateral:
.........A
.
.
........O
.
B
...............C
The quadrilateral (four sided polygon) formed by vertices A,B,O and C is non-convex.
You can see that if we choose two arbitrary points on the quadrilateral ABOC, say, P=B and Q=C (for simplicity), we immediately see that a line joining P and Q does NOT cut through the area of the polygon (quadrilateral rather). In this case, we say that it's not convex.
