1Say whether each statement is true or false, and rewrite the false ones correctly.
(a) The interior angles of a triangle add up to 360 degrees.
(b) All the angles of an equilateral triangle are equal.
(c) All the angles of an isosceles triangle are equal.
(d) The base angles of a right angled isosceles triangle are 60 degrees each.
2In a triangle PQR the angle Q is 60 degrees and the angle R is 30 degrees. Find the angle P.
3In a triangle ABC the angle B is a right angle and AB equals BC. Find the other two angles.
4In a triangle XYZ the sides XY and XZ are equal and the angle X is 44 degrees. Find the angles Y and Z.
5The three angles of a triangle are \( 2x \), \( 6x \) and \( x \). Find the value of x and the size of each angle.
6The vertex angle of an isosceles triangle is 70 degrees. Find its base angles.
7In a triangle ABC the angle BAC is 45 degrees and the angle ABC is twice the angle BCA. Find the angles ABC and BCA, and say what kind of triangle it is.
8The interior angles of a triangle are in the ratio 2:3:4. Find the three angles.
9In a triangle ABC the angle BAC is 30 degrees, the angle ABC is 75 degrees, AB is (2x + 1) cm and AC is 9 cm. Find the value of x.
10Say whether each statement is true or false, and rewrite the false ones correctly.
(a) Every rhombus is a square.
(b) In a kite the short diagonal bisects the long diagonal.
(c) The diagonals of a rhombus bisect each other.
(d) In a trapezium both pairs of opposite sides are parallel.
11In a rhombus PQRS the side PS is 4 cm, PQ is (x + 1) cm, QR is (y - 2) cm and SR is (z - 5) cm. Find x, y and z.
12In a rhombus ABCD the angle A is 80 degrees. Find the angles B, C and D.
13A rhombus ABCD has sides of 5 cm and half of its diagonal BD measures 4 cm. Find the length of the diagonal AC.
14In a kite ABCD the lengths AD = 5 cm, PD = 4 cm and DC = 9 cm are known, where P is the point where the diagonals cross. Find AB, BP and BC.
15The diagonals of a kite ABCD cross at the point P. What is the size of each of the four angles at P, and why?
16Construct a rectangle ABCD with AB = 7 cm and AD = 4 cm, and write down the steps.
17Find the size of one interior angle of a regular polygon when the number of sides (n) is: (a) n = 10, (b) n = 12.
18Find the size of one exterior angle of a regular polygon when the number of sides (n) is: (a) n = 6, (b) n = 9.
19Find the sum of the interior angles and the sum of the exterior angles of a polygon with n = 11.
20Working in a group of four or five, make a kite. Study the shapes used in it and present the steps of making it to the class.
21Each interior angle of a regular polygon is 150 degrees. How many sides does it have?
22Why can a square be called a rhombus and a rectangle at the same time?
23In a trapezium ABCD the sides AB and DC are parallel and the angle DAB is 110 degrees. Find the angle ADC.
24The interior angles of a polygon add up to 1440 degrees. Find the number of sides, and the number of triangles formed by drawing diagonals from one vertex.