Page 58 - MAT KS3 Y8 Cambridge CheckPoint

5.2 Explaining angle properties

5 The diagram shows a quadrilateral with a reflex angle. E
Show that the four angles add up to 360 °.
Divide it into two triangles
H F

G

6 In the diagram, PBC is a straight line. AQ is parallel to PC. A Q
a Explain why y = c. y°
a°
b Explain why x = a + y.
c Use your answers to parts a and b to show that, in triangle
x ° b ° c °
ABC, the exterior angle at B is equal to the sum of the two
interior opposite angles. P B C

7 In the diagram, PRT is a straight line. P
Q
a d° a° b°
x is the exterior angle of a triangle so a +
b = x
c°
Which triangle is Jake using? e° f ° x° R
S y°
b Write down a similar equation for the angle marked y.
c Use your answers to parts a and b to show that the angles
T
of quadrilateral PQRS add up to 360 °.

C
8 In the diagram, DX is parallel to BC. B
ZD is parallel to AB.
BDY is a straight line. D X
a Explain why angles BAD and ADZ are equal. A
b Explain why angles ABD and ZDY are equal. Y
c Use the diagram to show that the angles of quadrilateral Z
ABCD add up to 360 °. Do not use the fact that
the angle sum of a triangle is 180 °.
Use the angle at D.

56 5 Angles