Properties of 2D Shapes：练习题

Which of the following quadrilaterals has exactly two lines of symmetry and rotational symmetry of order 2?

If the sum of the interior angles of a regular polygon is \( 1800^{\circ} \), find the number of sides of the polygon.

Consider a regular polygon where the sum of its interior angles is 10 times the size of one of its exterior angles. Let \( n \) be the number of sides of this polygon. Find the value of \( n \) and determine the name of the polygon.

In the figure, \( ABCDE \) is a regular pentagon. Find the size of each interior angle.

In the figure, \( ABCD \) is a kite where \( AB = AD \) and \( CB = CD \). If \( \angle ABC = 110^{\circ} \) and \( \angle BCD = 40^{\circ} \), find the size of \( \angle BAD \).

State the number of lines of symmetry of an isosceles trapezoid that is not a parallelogram. <\/p>

In the figure, \( ABCD \) is a parallelogram. If \( \angle ABC = 115^{\circ} \) and \( \angle DAC = 35^{\circ} \), find the size of \( \angle ACD \).<\/p>

A regular polygon has an interior angle of \(144^{\circ}\). How many sides does this polygon have?

Consider a polygon where the sum of its interior angles is twice the sum of its exterior angles.
(a) Find the number of sides of this polygon.
(b) What is the name of this polygon?

In the figure, \( ABCD \) is a parallelogram. Given that \( \angle DAB = (3x + 10)^{\circ} \) and \( \angle ABC = (2x - 20)^{\circ} \).
(a) Find the value of \( x \).
(b) Find the size of \( \angle BCD \).
(c) If \( E \) is a point on \( AB \) such that \( \triangle ADE \) is an equilateral triangle, find \( \angle EDC \).