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Mixed exercises
{{exercise_number}}. What type of angles are \latex{\beta} and \latex{\gamma}, if \latex{\alpha} is an acute angle?
\latex{\alpha}
\latex{\beta}
\latex{\gamma}
{{exercise_number}}. The outside of a leather soccer ball consists of regular pentagon and hexagon shapes shown in the image. Measure their angles. (→)
\latex{\varepsilon}
\latex{\alpha}
\latex{\beta}
\latex{\gamma}
\latex{\delta}
\latex{\mu}
\latex{\theta}
\latex{\eta}
\latex{\nu}
\latex{\kappa}
\latex{\lambda}
{{exercise_number}}. List cardinal and intercardinal directions that form an angle of
a) \latex{ 90 }°;
b) \latex{ 180 }°;
c) \latex{ 45 }°;
d) \latex{ 135 }°;
e) \latex{ 225 }°.
{{exercise_number}}. A boat leaving the harbour sails \latex{ 5 } \latex{ km } in the northern direction, then turns towards the east and goes another \latex{ 5 } \latex{ km }. Draw the path of the boat in your notebook (\latex{ 1 } \latex{ cm } should correspond to \latex{ 1 } \latex{ km }). In which direction is it currently found compared to the harbour?
{{exercise_number}}.
a) Draw a right-angled triangle on quad paper. One of the legs should be three squares, while the other should be four squares. Measure its angles.
b) Draw a triangle whose sides are twice as long as those of the previously constructed triangle. Measure its angles.
c) Draw a triangle whose sides are three times as long as the sides of the first triangle. Measure its angles.
b) Draw a triangle whose sides are twice as long as those of the previously constructed triangle. Measure its angles.
c) Draw a triangle whose sides are three times as long as the sides of the first triangle. Measure its angles.
Compare the angles of the three triangles.
{{exercise_number}}. By what type of angle does the minute hand of a clock turn in
a) a quarter of an \latex{ hour };
b) forty-five \latex{ minutes };
c) half an \latex{ hour };
d) twenty \latex{ minutes? }
b) forty-five \latex{ minutes };
c) half an \latex{ hour };
d) twenty \latex{ minutes? }
{{exercise_number}}. Measure the angles of the triangle and the quadrilateral, and then calculate the sum of their interior angles.
\latex{\gamma}
\latex{\alpha}
\latex{\beta}
\latex{\varphi}
\latex{\delta}
\latex{\varepsilon}
\latex{\eta}
{{exercise_number}}. Measure the angles defined by the following points.
d) CDA \latex{\measuredangle}
a) ABC \latex{\measuredangle}
b) DAC \latex{\measuredangle}
c) ABD \latex{\measuredangle}
{{exercise_number}}. How much does the minute hand of a clock turn in \latex{ degrees } in
a) a quarter of an \latex{ hour };
b) half an \latex{ hour };
c) forty-five \latex{ minutes };
d) twenty \latex{ minutes ?}
{{exercise_number}}. How much does the hour hand of a clock turn in \latex{ degrees } in
a) two \latex{ hours };
b) one \latex{ hour };
c) half an \latex{ hour };
d) twenty \latex{ minutes?}
Construct these angles using a protractor.
{{exercise_number}}. Draw the face of a clock using a compass and a protractor.
{{exercise_number}}. What is the difference in \latex{ degrees } between the northern and intercardinal directions?
{{exercise_number}}. A tourist starts walking east, and after \latex{ 5 } \latex{ km }, he decides to take a \latex{ 45 }-\latex{ degree } turn to the right and continues walking for \latex{ 3 } \latex{ km }. After that, he takes a \latex{ 60 }-\latex{ degree } turn to the left and walks for \latex{ 4 } \latex{ km }. Draw the path of the tourist in your notebook (\latex{ 1 } \latex{ cm } should correspond to \latex{ 1 } \latex{ km }). How far did he get from the starting point? Measure it in your notebook.
{{exercise_number}}. Which of the following statements are true? Which ones are false?
a) The sum of two acute angles is always an acute angle.
b) Half an acute angle is always an acute angle.
c) Half an obtuse angle is certainly an acute angle.
d) Half a reflex angle cannot be an acute angle.
e) The sum of two obtuse angles is certainly a reflex angle.
b) Half an acute angle is always an acute angle.
c) Half an obtuse angle is certainly an acute angle.
d) Half a reflex angle cannot be an acute angle.
e) The sum of two obtuse angles is certainly a reflex angle.
{{exercise_number}}. Draw the following angles: \latex{\alpha,\beta, \alpha+\beta, \alpha-\beta} if
a) \latex{\alpha=\mathrm{65}_{}^{\circ }} and \latex{\beta=\mathrm{25}_{}^{\circ }};
b) \latex{\alpha=\mathrm{165}_{}^{\circ }} and \latex{\beta=\mathrm{45}_{}^{\circ }};
c) \latex{\alpha=\mathrm{235}_{}^{\circ }} and \latex{\beta=\mathrm{75}_{}^{\circ }}.
b) \latex{\alpha=\mathrm{165}_{}^{\circ }} and \latex{\beta=\mathrm{45}_{}^{\circ }};
c) \latex{\alpha=\mathrm{235}_{}^{\circ }} and \latex{\beta=\mathrm{75}_{}^{\circ }}.
Measure angles \latex{\alpha+\beta} and \latex{\alpha-\beta}. Perform calculations to check whether your drawing was accurate. What is the difference between the measured and calculated values?
{{exercise_number}}. Three times what angle is \latex{ 30 }° less than a straight angle?
{{exercise_number}}. During a survey, \latex{ 120 } fifth-graders had to answer three questions. The answers are shown in the pie charts below. Estimate how many students answered 'no' to each question. Check your estimations by measuring and performing calculations.
no
yes
Have you visited the dentist
in the last six months?
in the last six months?
Do you wear
braces?
braces?
Do you wash your
teeth every day?
teeth every day?
