Angles, lines and shapesTo learn to draw and measure angles

in shapes and lines

Types of Angles

A reflex angle ismore than 180°

A right angle

equals 90°

90°

An acute angle

is less than 90°

An obtuse angle ismore than 90° but less than 180°

b

b

a

acb

a

d

c

b

a

Angle Properties

Angles at a point add to 360°

a + b + c + d = 360°

Angles on a straight line add to 180°.

a + b + c = 180°

Vertically opposite angles are equal.

d

d

c

cb

b

a

a

Parallel Lines

Alternate angles are equal. Corresponding angles

are equal.

f

e

Interior angles add to 180°.

e + f = 180°

Triangles

c

ab

The sum of the angles of a triangleis 180°

a + b + c = 180°

Equilateral triangles have 3 equal sides and 3 equal angles.

a

a

Isosceles triangles have 2 equal sides and 2 equal angles.

60°

60° 60°

Exterior angles of a triangle

The exterior angle of a triangle is equal to the sum of the interior opposite angles.

interior opposite angles

exterior angle

A

B C D

i.e. ACD = ABC + BAC

Wassily Kandinsky

• Born in Moscow in 1866• Took up the study of art in earnest at age 30, moving

to Munich to study drawing and painting. • Trained musician, Kandinsky approached color with a

musician’s sensibility. • Had an obsession with Monet, which led him to

explore his own creative concepts of colour on canvas, which were sometimes controversial among his contemporaries and critics

• Little of the work Kandinsky produced in Russia has survived, although many of the paintings he created in Germany are still extant.

• In recent years, his artwork has sold for well over $20 million.

Task 1

Look at the following painting Wassily Kandinsky.

Kandinsky used a lot of shape throughout his art.

Using this painting, identify how many shapes and lines he has

used. If you have a protractor, measure some of the angles. If not

Can you identify any acute, obtuse, reflex and right angles he has used.

Task 2

Now try creating your own drawing using shape. You can use colour afterwards.

You should use the following shapes in your picture. You can use as many as you want of each shape. Remember to use a ruler to draw straight lines, protractor for circles (if you have one) and triangles.

• A circle

• A semi-circle

• A square

• A rectangle

• A quadrilateral with all sides of different lengths

• An equilateral triangle

• A right-angled triangle

• An isosceles triangle (two equal sides)

• A scalene triangle (with no equal sides and no equal angles)

• You can try including 3D shapes too, if you like!

• Parallel lines

• Some angles (at least one acute and obtuse angle). Optional: vertically opposite angles