Question

part b: by degree
the other type of circle graph is divided into 360 equal sections, because there are 360° in a whole circle. it is easy to use angles to create this type of circle graph.

1. the circle is divided into 8 sections. shade one in.

a) 360°÷8 = ____. therefore each section is ____°.
b) divide the circle into 4 sections, by shading in a quarter. 360°÷4 = ____. therefore each section is __°. write another math name for this angle. ____
c) divide the circle into two sections, by shading half. 360°÷2 = ____. therefore each section is ____°.

1. a compass rose is a circle marked to show directions relative to north. maps usually have a compass rose or an arrow to show which way is north.

a) write in the main directions on the compass rose. (hint news)
b) the direction halfway between north and east is called northeast. write in ne on the compass rose. it is ______ degrees from the horizontal.
c) label the directions nw, se, and sw on the compass rose.
d) what is the angle between nw and sw? ______
e) what is the angle between sw and ne? ______
f) what is the angle between s and se? ______
unit 2 - proportional reasoning - 4 - mat2l

Explanation:

Step1: Calculate angle for 8 - section circle

$360^{\circ}\div8 = 45^{\circ}$. So each section is $45^{\circ}$.

Step2: Calculate angle for 4 - section circle

$360^{\circ}\div4=90^{\circ}$. Each section is $90^{\circ}$, and another name for this angle is a right - angle.

Step3: Calculate angle for 2 - section circle

$360^{\circ}\div2 = 180^{\circ}$. Each section is $180^{\circ}$.

Step4: Compass rose directions

a) The main directions on the compass rose are North (N), East (E), South (S), West (W).
b) The direction Northeast (NE) is $45$ degrees from the horizontal.
c) Label NW (Northwest), SE (Southeast), and SW (Southwest) on the compass rose as per the compass - rose convention.
d) The angle between NW and SW is $90^{\circ}$.
e) The angle between SW and NE is $180^{\circ}$.
f) The angle between S and SE is $45^{\circ}$.

Answer:

1.
a) $45$, $45$
b) $90$, $90$, right - angle
c) $180$, $180$
2.
a) North (N), East (E), South (S), West (W)
b) $45$
c) Labeled as per compass - rose convention
d) $90^{\circ}$
e) $180^{\circ}$
f) $45^{\circ}$