Polygons

If $x+y+z+w=k°$ then the value of $k$ is

From the figure, if $x+y+z=k°$ then the value of $k$ is

Find the value of $x$ in the given figure.

The angle measure in the given figure is $x°$. Find the value of $x$.

If each angle in the given figure, measure $x°$, then find the value of $x$.

Find the angle measure of $x$ in the given figure.

What is a regular polygon? State the name of a regular polygon of $6$ sides.

What is a regular polygon? State the name of a regular polygon of $4$ sides.

Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)

Figure
Side	$3$	$4$	$5$	$6$
Angle	$180°$	$2\times 180°$ $=(4-2)\times 180°$	$3\times 180°$ $=(5-2)\times 180°$	$4\times 180°$ $=(6-2)\times 180°$

If the angle sum of a convex polygon with number of sides equal to $8$ is $k°$, then find the value of $k$.

Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)

Figure
Side	$3$	$4$	$5$	$6$
Angle	$180°$	$2\times 180°$ $=(4-2)\times 180°$	$3\times 180°$ $=(5-2)\times 180°$	$4\times 180°$ $=(6-2)\times 180°$

If the angle sum of a convex polygon with number of sides equal to $10$ is $k°$, then find the value of $k$.

Examine the table. Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)

Figure
Side	$3$	$4$	$5$	$6$
Angle	$180°$	$2\times 180°$ $=(4-2)\times 180°$	$3\times 180°$ $=(5-2)\times 180°$	$4\times 180°$ $=(6-2)\times 180°$

Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)

Figure
Side	$3$	$4$	$5$	$6$
Angle	$180°$	$2\times 180°$ $=(4-2)\times 180°$	$3\times 180°$ $=(5-2)\times 180°$	$4\times 180°$ $=(6-2)\times 180°$

How many diagonals does a triangle have?

How many diagonals does the following figure have?

A regular hexagon.

How many diagonals does a Convex quadrilateral have?

What is a regular polygon? State the name of a regular polygon of $3$ sides.

What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)