Page 59 - Mathematics Coursebook

5.3 Calculating angles

5.3 Calculating angles

Important angle facts
$e angles round a point add up to 360°. x°

$e angles on a straight line add up to 180°.
z°

$e three angles of a triangle add up to 180°. y°
x + y + z = 180

A four-sided shape is called a quadrilateral.
What can you say about the angles of a
quadrilateral?
By adding another line, you can divide the
quadrilateral into two triangles.

$e six angles of the two triangles
combine to make up the four angles of The angles in each
the quadrilateral. triangle add up to 180°.
$e angles of a quadrilateral add up to 2 × 180° = 360°.

Worked example 5.3

Three of the angles of a four-sided shape are equal to 85°. How big is the fourth angle?

3 × 85° = 255° All four angles add up to 360°. The three angles given add up to 255°.
The fourth angle is 105°. The fourth angle is 360° – 255° = 105°.

) Exercise 5.3

1 Calculate the sizes of the lettered angles.

34°

116° a° 55° c° d°
b° 60° 24°

2 Calculate the sizes of the lettered angles.

130°
120° a°
155° 37°
68° 52°
b° 36° 42° d°
c°

58 5 Angles