1. What angles greater than 180 could be measured? 10°
GM1.1 Core Starter
What sizes of angles (from 0 to 180) can you measure with this semi-circular measurer?
What angles greater than 180 could be measured?
10°
30°
90°
Preamble
Pupils should be encouraged to explain not only how they would measure each angle, but also the system that they use to make sure that every possible angle is found. It will be necessary to establish at the outset that only angles formed by combinations of adjacent sectors are allowed.
Possible content
Angle facts.
Resources
Some pupils may benefit from a copy of the measurer. A copy on a transparency may be useful for demonstrating to the whole class how the measurer can be used.
Solution/Notes
The following angles up to 180 can be measured.
180° 30° 10° 90° 20° (= 180° – 30° – 30° – 10° – 90°) 60° (= 30° + 30°) 70° (= 30° + 30° + 10°) 160° (= 30° + 30° + 10° + 90°) 40° (= 30° + 10°) 130° (= 30° + 10° + 90°) 150° (= 30° + 10° + 90° + 20°) 100° (= 10° + 90°) 120° (= 10° + 90° + 20°) 110° (= 90° + 20°).
For angles greater than 180°, any angle of the form 180° + a or 360° − a can be measured, where a is one of the angles listed above.
Original Material © Cambridge University Press 2009
Original Material © Cambridge University Press 2009