x = 80^o, y = 100^o, z = 80^o

38 cm

ㄥA = 90°, ㄥF = 60°, ㄥC = 30°

11

We have, n=12
Each interior angle = \(\frac { { 180 }^{ 0 }\times (n-2) }{ n } =\frac { { 180 }^{ 0 }\times (12-2) }{ 12 } =\frac { { 1800 }^{ 0 } }{ 12 } \)=150⁰

In \(\Delta\)COD,  we have \(\angle\)COD + \(\angle\)1 + \(\angle\)2 = 180^o
\(\Rightarrow\) \(\angle\)COD = 180^o - [\(\angle\)1 + \(\angle\)2]
\(\Rightarrow\)\(\angle\)COD = 180^o - \(\left[ \frac { 1 }{ 2 } \angle D+\frac { 1 }{ 2 } \angle C \right] \)
\(\Rightarrow\) \(\angle\)COD = 180^o - \(\frac { 1 }{ 2 } \left[ \angle D+\angle C \right] \)
But \(\angle\)A + \(\angle\)B + \(\angle\)C + \(\angle\)D = 360^o
\(\Rightarrow\) \(\angle\)C + \(\angle\)D = 360^o - (\(\angle\)A + \(\angle\)B )
\(\therefore\)\(\angle\)COD = 180^o - \(\frac { 1 }{ 2 } \)[360^o - (\(\angle\)A + \(\angle\)B)
= 180^o - \(\frac { 1 }{ 2 } \)[360^o] + \(\frac { 1 }{ 2 } \)[\(\angle\)A + \(\angle\)B]
= 180^o - 180^o + \(\frac { 1 }{ 2 } \)(\(\angle\)A + \(\angle\)B) = \(\frac { 1 }{ 2 } \)(\(\angle\)A + \(\angle\)B)
Thus, \(\angle\)COD = \(\frac { 1 }{ 2 } \)[\(\angle\)A + \(\angle\)B]

Since, the sum of the measures of interior angles of a quadrilateral is 360°.

Also, 115° + 70° + 60° = 245°
\(\therefore\)245° + LABC = 360°
\(\Rightarrow\)\(\angle \)ABC = 360° - 245° = 115°
Now, x = ext. \(\angle\)BCD = 180° - \(\angle\)BCD
= 180° - 115° = 65°
Similarly, y = 180° - 70° = 110°
z = 180° - 60° = 120°
w = 180° - 115° = 65°
\(\therefore\)x +y + z + w = 65° + 110°+ 120° + 65° = 360°

On arranging the four copies of congruent cardboard as shown in the given figure, we see that ㄥ1, ㄥ2, ㄥ3 and ㄥ4 meet at a point.
We know that, at a point, we get a complete angle whose value is 360°.
So, the sum of the angles ㄥ1, ㄥ2, ㄥ3 and ㄥ4 is 360°.
i.e, mㄥ1 + mㄥ2 + mㄥ3 + mㄥ4 = 360° ... (i)
Also, ㄥ1 = ㄥA, ㄥ2 = ㄥB, ㄥ3 = ㄥC and ㄥ4 = ㄥD
From Eq. (i), we get
ㄥA + ㄥB + ㄥC + ㄥD = 360°
Hence, the sum of the measures of the four angles of a quadrilateral is 360°.

(l)\(\rightarrow\)VERTICES
(2)\(\rightarrow\)HEXAGON
(3)\(\rightarrow\)EDGE
(4)\(\rightarrow\)QUADRILATERAL
(5)\(\rightarrow\)PENTAGON
(6)\(\rightarrow\)RHOMBUS
(7)\(\rightarrow\)POLYGON
(8)\(\rightarrow\)DIAGONAL

(a) Simple curve A plane figure formed by joining a number of points without lifting a pencil from the paper and without returing any portion of the drawing other than single points is called a simple curve or curve. In the given figures, simple curves are figures (i), (ii), (v), (vi) and (vii).
(b) Simple closed curve A closed curve, which does not intersect itself, is called a simple closed curve. In the given figures, simple closed curves are figures (i), (ii), (v), (vi) and (vii).
(c) Polygon A polygon is a closed curve formed by the line segments such that
(i) no two line segments intersect except at their end points.
(ii) no two line segments with a common end points are coincide. In other words, a simple dosed curve made upto only line segments is called a polygon. In the given figures, polygons are figures (i) and (ii).
(d) Convex polygon A convex polygon is a polygon in which each interior angle has a measure less than 180°. In other words, a polygon is convex, if noportion of their diagonals in their exterior. In the given figures, convex polygon is figure (ii).
(e) Concave polygon A concave polygon is a polygon, which atleast one interior angle has measure more than 180°, i.e. atleast one segment connecting two vertices is outside the polygon. In the given figure, concave polygons are figures (i) and (iv).

Required measure = \({360^\circ-(110^\circ+100^\circ)\over 2}=75^\circ\)

8 cm; [∵ in a rectangle, diagonals are of equal length]

Square; since, in a square all the sides and angles are equal.