Calculate the fourth angle of the quadrilateral whose other three angles are 100°, 60° and 80°.

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4. Fourth angle of a quadrilateral

Step 1: Recall the sum of angles in a quadrilateral.
The sum of the interior angles of any quadrilateral is $360^\circ$.

Step 2: Calculate the fourth angle.
Let the fourth angle be $x$.

$$x + 100^\circ + 60^\circ + 80^\circ = 360^\circ$$ $$x + 240^\circ = 360^\circ$$ $$x = 360^\circ - 240^\circ$$ $$x = 120^\circ$$

The fourth angle of the quadrilateral is $\boxed{120^\circ}$.

5. Size of each angle of a regular decagon

Step 1: Determine the number of sides of a decagon.
A decagon is a polygon with 10 sides, so $n=10$.

Step 2: Calculate the sum of interior angles.
The sum of the interior angles of a polygon with $n$ sides is given by the formula $(n-2) \times 180^\circ$.

$$\text{Sum of angles} = (10-2) \times 180^\circ$$ $$\text{Sum of angles} = 8 \times 180^\circ$$ $$\text{Sum of angles} = 1440^\circ$$

Step 3: Calculate the size of each angle.
For a regular polygon, all interior angles are equal. Divide the sum of angles by the number of sides.

$$\text{Each angle} = \frac{1440^\circ}{10}$$ $$\text{Each angle} = 144^\circ$$

The size of each angle of a regular decagon is $\boxed{144^\circ}$.

6. What is a polygon?

A polygon is a closed two-dimensional shape made up of straight line segments connected end-to-end. The line segments do not cross each other, and the shape encloses a single region.

7. Angle between directions