Page 61 - MAT KS3 Y8 Cambridge CheckPoint

5.3 Solving angle problems

8 In the diagram, two of the sides of the quadrilateral have been extended.
a Show that w + y = a + b + c + d. w°
c°
d°

a° b°
y°

In this diagram, all of the sides of the quadrilateral have been extended.
b Show that w + x + y + z = 360 °. w°
x°

Use the result of part a.

z° y°

9 Look at the diagram of the irregular five-pointed star. a°
a Explain why x = b + d.
b Explain why y = c + e. e° x° y°
c Show that the sum of the angles in the points of the star, b°
a + b + c + d + e, is 180 °.

d°

c°

Summary

You should now know that: You should be able to:
★ You can identify the special properties of parallel ★ Identify alternate and corresponding angles.
lines and transversals, including corresponding ★ Understand a proof that the angle sum of a
angles and alternate angles. triangle is 180°.
★ Corresponding angles are equal. ★ Understand a proof that the angle sum of a
★ Alternate angles are equal. quadrilateral is 360°.
★ Every vertex of a triangle has an exterior angle. ★ Understand a proof that the exterior angle of a
★ A proof using a logical argument is different from triangle is equal to the sum of the two interior
opposite angles.
a demonstration.
★ You can prove the angle sum of a triangle is 180° ★ Solve geometrical problems using properties of
angles, of parallel and intersecting lines, and of
and the angle sum of a quadrilateral is 360°.
triangles and special quadrilaterals, explaining
★ You can explain your reasoning when you solve a
reasoning with diagrams and text.
geometric problem.
★ Recognise and use spatial relationships in two
dimensions.
★ Use logical arguments to interpret the
mathematics in a context or to establish the
truth of a statement.

5 Angles 59