Foundations of Mathematics 11
Find the missing angle and state the reason for each answer. (1 mark for answer and reason)
1.
2.
3.
4.
5.
isos Δ plus supp 's
1 =
110
2 =
35
1 =
55
vert opp  ' s plus sum of Δ
2 =
65
sum of Δ = 180
3 =
30
alternate interior angles
4 =
120
supplementary angles
sum of Δ 180 plus isos 
30
sum of Δ 180 plus isos ,
co-interior angles
2 =
75
sum of Δ 180 angles on a line
or alternate interior angles
1 =
110
sum of Δ 180
2 =
40
sum of Δ 180
1 =
120
isos Δ plus sum of   180
2 =
60
sum of Δ 180 plus co-interior angles
1 =
Foundations of Mathematics 11
8.
BC
EF
given
2  3
corresponding s
1  3
given
1  2
both  to 3
AB
corresponding s 
DE
4 marks
9.
AB
CD
2  3
1  2
given
alternate interior s
given
1  3
substitution
AC  AB
isosceles triangle definition
4 marks
Foundations of Mathematics 11
10.
AB
CD
given
2  3
alternate interior s
3  4
vertically opp s
1  4
given
1  2
substitution
4 marks
11. The sum of degrees of a 15-sided polygon is:
 n  2 180
15  2 180
13180
n  15
2340
2340
11) _____________________________
2 marks
12. Find the number of sides of a regular polygon with an interior angle of 162°.
n
 2 180
 162
n
 n  2 180  162n
180n  360  162n
180n  162n  360
18n  360
18n
360

18
18
n  20
n  20
12) _____________________________
2 marks
Foundations of Mathematics 11
13. A regular polygon has 15 sides. Find the measure of each angle.
n




 2 180
n  15
n
15  2 180
15
13180
15
2340
15
156
156
13) _____________________________
2 marks
14. The sum of the interior angles of a regular polygon is 3060°. Find the exterior angle.
 n  2 180
 3060
180n  360  3060
180n  3420
180n
180
360
n  19
n
360
18.9
19
3420
180
n  19

18.9
14) _____________________________
2 marks
15. Find the number of sides of a regular polygon with an exterior angle of 20°.
360
n
 20
360
20
n  18
n 
n  18
15) _____________________________
2 marks