问题1.这里有一些数字：
根据以下内容对它们进行分类。
(a)简单曲线(b)简单闭合曲线(c)多边形(d)凸多边形(e)凹多边形
解决方案：
a) 1, 2, 5, 6, 7
b) 1, 2, 5, 6, 7
c) 1, 2
d) 2
e) 1
问题2：以下每个对角线有多少对角线?
(a)凸四边形
解决方案：
Here we can see that only two diagonals are possible for the convex quadrilateral.
Answer: 2
(b)正六边形
解决方案：
Here we can see that only three diagonals are possible for the convex quadrilateral.
Answer: 3
(c)三角形
解决方案：
In case of a triangle no diagonal is possible.
Answer: 0
问题3.凸四边形的角度的量度之和是多少?如果四边形不是凸的，此属性是否成立?
解决方案：
Sum of the angles of a quadrilateral is always 180°. It doesn’t depend on whether the quadrilateral is a convex or a concave.
问题4.检查表。 (每个图都分成三角形，并由此得出角度的总和)。
关于具有边数的凸多边形的角度和，您能说什么?
解决方案：
From the above given table we can deduce that for a given number of sides n the sum of the angles of a convex polygon is (n – 2) × 180°.
a) 7
Ans: (7 – 2) × 180° = 5 × 180° = 900°
b) 8
Ans: (8 – 2) × 180° = 6 × 180° = 1080°
c) 10
Ans: (10 – 2) × 180° = 8 × 180° = 1440°
d) n
Ans: (n – 2) x 180°
问题5.什么是规则多边形?说明以下规则多边形的名称：(i)3面(ii)4面(iii)6面
解决方案：
Regular Polygon is a polygon with equal sides and equal angles.
(i) 3 sides : Equilateral triangle
(ii) 4 sides : Square
(iii) 6 sides : Regular Hexagon
问题6.在下图中找到角度量度x。
解决方案：
a) Total sum of the angles of the quadrilateral = 360°
Therefore, 50° + 130° + 120° + x = 360° ⇒ 300° + x = 360° ⇒ x = 60°
b) Total sum of the angles of the quadrilateral = 360°
Therefore, 60° + 70° + 90° + x = 360° ⇒ 220° + x = 360° ⇒ x = 140°
c) Total sum of the angles of the polygon = 540°
Angles adjacent to 60° = 180° – 60° = 120°
Angles adjacent to 70° = 180° – 70° = 110°
Therefore, 110° + 30° + 120° + x + x= 540° ⇒ 260° + 2x = 540° ⇒ 2x = 280° ⇒ x = 140°
d) Total sum of the angles of the polygon = 540°
Therefore, x° + x° + x° + x° + x°= 540° ⇒ 5x = 540° ⇒ x = 108°
问题7.(a)求x + y + z(b)求x + y + z + w
解决方案：
(a) By exterior angle property, y = 90° + 30° = 120°
x = 180° – 90° = 90°
z = 180° – 30° = 150°
So, the answer x + y + z = 360°
(b) Angle adjacent to w = 360° – ( 60° + 80° + 120° ) = 100°
By Adjacent Angle property,
w = 180° – 100° = 80°
x = 180° – 120° = 60°
y = 180° – 80° = 100°
z = 180° – 60° = 120°
So, the answer w + x + y + z = 360°