Question: Birlik International School
Final exam preparation worksheet – Grade 9
1 Work out the values of $a$, $b$ and $c$.
49°
$a$°
$c$°
83°
$b$°
2 Work out the value of $a$. Explain your method.
$a$°
62°
105°
53°
3 The diagram shows two parallel lines and two other straight lines.
145°
$x$°
43°
NOT TO
SCALE
Find the value of $x$.
4 A nonagon is a polygon with 9 sides.
a) Work out the sum of the interior angles of a nonagon.
b) Work out the interior angle of a regular nonagon.
5 The sum of the interior angles of a polygon is 900°.
How many sides does the polygon have?
6 The graph shows the cost of different masses of lemons.
cost ($)
16
14
12
10
8
6
4
2
0
0 1 2 3 4 5
mass (kg)
Work out the cost of 6 kg of lemons.
1. **Problem:** Work out the values of $a$, $b$, and $c$ in the angle diagram with angles $49^\circ$, $a^\circ$, $c^\circ$, $83^\circ$, and $b^\circ$.
2. **Formula and rules:** Angles on a straight line sum to $180^\circ$. Vertically opposite angles are equal. Angles around a point sum to $360^\circ$.
3. **Step-by-step solution:**
- Since $49^\circ$ and $a^\circ$ are on a straight line, $49^\circ + a^\circ = 180^\circ$.
- So, $$a = 180 - 49 = 131^\circ.$$
- Angles $a^\circ$ and $b^\circ$ are vertically opposite, so $$b = a = 131^\circ.$$
- Angles $c^\circ$ and $83^\circ$ are on a straight line, so $$c + 83 = 180.$$
- Therefore, $$c = 180 - 83 = 97^\circ.$$
**Final answers:** $a = 131^\circ$, $b = 131^\circ$, $c = 97^\circ$.