© t madas. what do the 3 angles of any triangle add up to? 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16...
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© T Madas
© T Madas
© T Madas
What do the 3 angles of any triangle add up to?
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
© T Madas
What do the 3 angles of any triangle add up to?
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
© T Madas
© T Madas
The angles in a triangle add up to 180°
© T Madas
The angles in a triangle add up to 180°
© T Madas
The angles in a triangle add up to 180°
© T Madas
© T Madas
Angle Calculations in Triangles
– 125° =55°180°
+ 50° =
125°75°
– 119° = 61°180°
+ 90° =
119°29°
75°
55°
50°
29°
61°
© T Madas
Angle Calculations in Triangles
÷ 2 = 70°140°
– 40° = 140°180°
– 70° =110°
180°
+ 35° =
70°35°
40°
70° 70°
35° 35°
110°
© T Madas
PracticeAngle Calculationswith Triangles
© T Madas
70°
60°
50°
55°
45°
80°
45° 35°
100°
25°
65°
65° 70°
45°
30°
35°115° 75°
55°
50° 35°
25°
120°
© T Madas
65°
70°
45°
52°
48°
80°
43° 33°
104°
29°
61°
62° 71°
47°
33°
38°109° 77°
52°
51° 39°
24°
117°
© T Madas
60°
80°
40°
53°
47°
80°
43° 36°
101°
26°
64°
61° 71°
48°
32°
38°110° 78°
52°
50° 40°
23°
117°
© T Madas
40°70°
55° 55° 65° 65°
50°
45°45°
35° 35°
110°80°
80°20°
70° 70°100°
40°
40°
© T Madas
Quick Test onAngle Calculationswith Triangles
© T Madas
70°
60°
50°
55°
45°
80°
45° 35°
100°
25°
65°
65° 70°
45°
30°
35°115° 75°
55°
50° 35°
25°
120°
© T Madas
65°
70°
45°
52°
48°
80°
43° 33°
104°
29°
61°
62° 71°
47°
33°
38°109° 77°
52°
51° 39°
24°
117°
© T Madas
60°
80°
40°
53°
47°
80°
43° 36°
101°
26°
64°
61° 71°
48°
32°
38°110° 78°
52°
50° 40°
23°
117°
© T Madas
40°70°
55° 55° 65° 65°
50°
45°45°
35° 35°
110°80°
80°20°
70° 70°100°
40°
40°
© T Madas
© T Madas
180°
180°
What do the 4 angles in a quadrilateral add up to?
360°
© T Madas
PracticeAngle Calculationswith Quadrilaterals
© T Madas
90° 95°
65°
110°
150°
50°100°
60°160°
40°110°
50°30°
95°
75°
160°
75°
105° 115°
65° 75°45°
80°
160°
155° 60°
115°30°
155°
70°
100°
35°
95°
95°
65°
105°
The angles of a quadrilateral add up to 360°
© T Madas
90° 95°
70°
105°
150°
45°100°
65°160°
45°110°
45°35°
95°
70°
160°
65°
115° 120°
60° 75°45°
75°
165°
150° 65°
115°30°
150°
75°
100°
35°
100°
95°
55°
110°
The angles of a quadrilateral add up to 360°
© T Madas
91° 92°
73°
105°
152°
46°97°
65°159°
44°111°
46°33°
94°
69°
164°
64°
114° 119°
63° 74°44°
74°
168°
149° 68°
115°28°
155°
72°
97°
36°
91°
92°
79°
98°
The angles of a quadrilateral add up to 360°
© T Madas
Quick Test onAngle Calculationswith Quadrilaterals
© T Madas
The angles of a quadrilateral add up to 360°
90° 95°
65°
110°
150°
50°100°
60°160°
40°110°
50°30°
95°
75°
160°
75°
105° 115°
65° 75°45°
80°
160°
155° 60°
115°30°
155°
70°
100°
35°
95°
95°
65°
105°
test
© T Madas
The angles of a quadrilateral add up to 360°
90° 95°
70°
105°
150°
45°100°
65°160°
45°110°
45°35°
95°
70°
160°
65°
115° 120°
60° 75°45°
75°
165°
150° 65°
115°30°
150°
75°
100°
35°
100°
95°
55°
110°
test
© T Madas
91° 92°
73°
105°
152°
46°97°
65°159°
44°111°
46°33°
94°
69°
164°
64°
114° 119°
63° 74°44°
74°
168°
149° 68°
115°28°
155°
72°
97°
36°
91°
92°
79°
98°
test
The angles of a quadrilateral add up to 360°
© T Madas
© T Madas
x
21°
29°
69° 61°
50°
Calculate the angle marked as x.
© T Madas
© T Madas
Calculate the angle marked as x
x
50°70°
130° 20°
30°
© T Madas
© T Madas
49°
x
41°
Calculate the angle marked as x.
49°
© T Madas
© T Madas
140° 40
°70°
70°
Calculate the three angles of the triangle
110° 70
°55°
55°
Calculate the angle marked with x
x
© T Madas
© T Madas
136°
44°
68°
68°
Calculate the angle marked with x
x292°
© T Madas
© T Madas
50°70°
55° 55°65° 65°
Calculate the missing angles in each triangle
© T Madas
© T Madas
One of the angles of a rhombus is 47°.Calculate the angle marked as x.
47°x
47°
• Opposite angles in a parallelogram are equal
• A rhombus is a special parallelogram• Angles in any quadrilateral add up to
360°
47+ 47
94
360– 94266
266 ÷ 2 =133°133°
© T Madas
© T Madas
One of the angles of an isosceles triangle is 64°.
What are the sizes of the other two angles?
[You must show that there are 2 different possibilities]
64° 64°
52° 64°
58° 58°
1st possibility 2nd possibility
64+ 64128
180– 128
52
116 ÷ 2 = 58°180
– 64116
© T Madas
© T Madas
A parallelogram ABCD, its diagonals and some of its angles are shown in the diagram below.
B
20°
50°55°
1. Calculate the four angles of the parallelogram.2. Using the properties of parallelograms (including
special parallelograms), explain why this drawing is impossible.
C
CAD = BCA: alternating angles
20°
DA
© T Madas
A parallelogram ABCD, its diagonals and some of its angles are shown in the diagram below.
D
B
20°
50°55°
1. Calculate the four angles of the parallelogram.2. Using the properties of parallelograms (including
special parallelograms), explain why this drawing is impossible.
20°
ACD = BAC: alternating angles
50°
we could use:
opposite angles in any parallelogram are equal
or
CAD = BCA: alternating angles
A
C
© T Madas
A parallelogram ABCD, its diagonals and some of its angles are shown in the diagram below.
D
B
20°
50°55°
1. Calculate the four angles of the parallelogram.2. Using the properties of parallelograms (including
special parallelograms), explain why this drawing is impossible.
20°
50°
A
C
70+ 70140
360– 140
220 220 ÷ 2 = 110°
we could use:
opposite angles in any parallelogram are equal
or
110°
© T Madas
In any parallelogram
both diagonals bisect their angles:
both diagonals do not bisect their angles:
only one diagonal bisect its angles:
Can you think of a quadrilateral where only one diagonal bisect its angles?
A parallelogram ABCD, its diagonals and some of its angles are shown in the diagram below.
D
B
20°
50°55°
1. Calculate the four angles of the parallelogram.2. Using the properties of parallelograms (including
special parallelograms), explain why this drawing is impossible.
20°
50°
A
C
110°
55°
, square
, ordinary parallelogram
rhombus
rectangle
NONE
there is no parallelogram with only one diagonal bisecting its angles
© T Madas