Name: _________________________________
Angles and triangles
January 26, 2015 – Monday / January 27, 2015– Tuesday / January 30, 2015 - Friday
1) A right triangle has one angle that measures
36°. Find the measure of the other acute
angle.
5) An isosceles triangle has a perimeter of 50 in.
Two of its sides have equal length, and the
third side is 5 in. longer than the other two
sides. What is the length of the third side?
2) A triangle has an area of 42 m2 and a base
length of 7 m. What is the height of the
triangle?
6) In Latoya’s class they are cutting out
snowflakes from square paper folded in half
and then in half again to make a folded
square. Latoya cuts along the three lines
shown in the picture of the folded square.
When she unfolds her paper what shape will
fall out of her square?
3) It is possible to split up an equilateral triangle
to make four smaller equilateral triangles as
shown in the first figure below. How would
you split up an equilateral triangle to make six
smaller equilateral triangles that exactly fill
the larger triangle and do not overlap? Note
that they need not all be the same size. Use
the empty triangle to work out your answer.
7) The smallest angle of a triangle is two-thirds
the size of the middle angle, and the middle
angle is three-sevenths of the largest angle.
Find all three angle measures.
4) A pinwheel is made of four identical shapes
each with a different color arranged
counterclockwise in color order red, blue,
green, and gold. They are evenly spaced. The
wind spins the pinwheel counterclockwise,
and when it stops, the red shape is now
where the blue shape used to be. If the
pinwheel went through two complete
rotations before red ended up where blue
used to be, how many total degrees did the
red shape travel?
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Cascade Ridge Elementary – Math Club
8) A triomino is an L-shaped figure made up of
three unit squares. Show how it is possible to
cover the figure (a 4 × 4 board with the
missing top corner square) with five
triominoes.
Name: _________________________________
Angles and triangles
January 26, 2015 – Monday / January 27, 2015– Tuesday / January 30, 2015 - Friday
BONUS PROBLEMS
9)
Right triangle ABC shown in the figure has a right angle at B and a 50° angle at A. Reflect
triangle ABC over side BC to create a new larger shape made up of two triangles. What’s the
measure of the new big angle at vertex C?
10) How many rectangles of any size can be found in the figure below?
11) If you use 120 one-inch by one-inch tiles to cover a rectangular floor whose length is 10 inches
and width is 12 inches, how many tiles will not touch the border of the floor?
12) The Pie Man always bakes his circular pies with a diameter of 12 inches and serves them in slices
that are 45 degrees at their vertex. What is the area, in square inches, of each slice? Express
your answer to the nearest whole square inch.
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Cascade Ridge Elementary – Math Club
Name: _________________________________
Angles and triangles
January 26, 2015 – Monday / January 27, 2015– Tuesday / January 30, 2015 - Friday
Solutions
Note: There are many acceptable strategies to solving each problem. This sheet shows just one
strategy.
1) The sum of the angles in any triangle is 180°.
The right angle is 90°.
Therefore the remaining angle is 180 – 90 – 36.
Answer: 54°
2) The area of a triangle is (base x height x
1
2
1
2
).
7 x h x = 42
So, h = 12
Answer: 12 meters
3) Answer:
4) Let S be the length of the first two sides.
S + S + (S + 5) = 50
3 x S = 45
S = 15
So, the third side is S + 5 = 15 + 5 = 20
Answer: 20 in.
5) Try it out!
Answer: Octagon (8-sided figure)
6) Let the three angles from smallest to largest be A, B, and C.
A + B + C = 180
A =
2
3
×B
B =
3
7
×C
Substituting one equation into another …
2 3
6
A = 3 × 7 × C = 21 × C
3
Cascade Ridge Elementary – Math Club
Name: _________________________________
Angles and triangles
January 26, 2015 – Monday / January 27, 2015– Tuesday / January 30, 2015 - Friday
6
3
6
9
36
21
× C = 180
(21 × C) + (7 × C) + C = 180
21
(21 × C) + (21 × C) + (21 × C) = 180
21
C = 180 × 36
C = 105
B =
3
7
×C =
2
3
7
× 105 = 45
2
A = 3 × B = 3 × 45 = 30
Answer: 30, 45, 105
7) Drawing the pinwheel:
Two full rotations = 2 x 360° = 720°
1
Additional of a rotation for red to end up where blue was = 90°
4
720 + 90 = 810
Answer: 810°
8) Answer:
9) Once you reflect the shape horizontally across side BC, you end up with this:
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Cascade Ridge Elementary – Math Club
Name: _________________________________
Angles and triangles
January 26, 2015 – Monday / January 27, 2015– Tuesday / January 30, 2015 - Friday
Since the sum of all three angles in any triangle must be 180°, the new larger angle at vertex C
must be 180 – 50 – 50 = 80°.
Answer: 80°
10) Break the problem down by counting the rectangles of various sizes:
4 wide x 3 tall
3 wide x 3 tall
2 wide x 3 tall
1 wide x 3 tall
4 wide x 2 tall
3 wide x 2 tall
2 wide x 2 tall
1 wide x 2 tall
4 wide x 1 tall
3 wide x 1 tall
2 wide x 1 tall
1 wide x 1 tall
1 rectangle
2 rectangles
3 rectangles
4 rectangles
2 rectangles
4 rectangles
6 rectangles
8 rectangles
3 rectangles
6 rectangles
9 rectangles
12 rectangles
TOTAL
60 rectangles
Answer: 60 rectangles
11) Drawing it out:
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Cascade Ridge Elementary – Math Club
Name: _________________________________
Angles and triangles
January 26, 2015 – Monday / January 27, 2015– Tuesday / January 30, 2015 - Friday
The inside tiles, those not touching the wall, form a 10x8 rectangle, so there are 80 tiles not
touching the wall.
Answer: 80 tiles
12) Each slice is 1/8 of the whole pie, because 45° is 1/8 of 360°. The area of a circle is:
Area = π × radius2
So, the area of the whole pie is:
Area of pie = π × 62
Area of pie = 113.097 in2
So, the area of one slice is:
1
8
Area of slice = × 113.097
Area of slice = 14.137 in2
Answer: 14 in2
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Cascade Ridge Elementary – Math Club