Question
The diagram shows the positions of three towns $A,B$ and $C.$
Angle $ABC=103^{\circ}.$
The bearing of town $B$ from town $A$ is 48°.
Town $C$ is due east of town $A.$
Find the bearing of town $C$ from town $B.$
▶️Answer/Explanation
$125$
- Angle \( ABC = 103^\circ \)
- Bearing of B from A = 48°
- C is due east of A, so the line AC is horizontal.
bearing of C from B.
- Bearing of B from A = 48°, so the angle between the north line at A and line AB is 48°.
- Since C is due east of A, the angle NAC = 90°.
So, the bearing of C from A = 90°.
The external angle at B is:
$
180^\circ – 103^\circ = 77^\circ
$
the bearing of C from B is measured clockwise from north,
add this 77° to the 48° bearing of B from A:
$
\text{Bearing of C from B} = 48^\circ + 77^\circ = 125^\circ
$
Question
The diagram shows an isosceles triangle.
Find the value of x.
▶️Answer/Explanation
$108$
it’s an isosceles triangle, the two base angles are equal. One base angle is given as 36°, so the other base angle is also 36°.
$
\text{Angle sum in a triangle} = 180^\circ
$
$
36^\circ + 36^\circ + x^\circ = 180^\circ
$
$
72^\circ + x^\circ = 180^\circ
$
$
x^\circ = 180^\circ – 72^\circ
$
$
x^\circ = 108^\circ
$
Question
(a) Measure the size of angle x.
(b) Measure the length of line AB in millimetres.
(c) Mark the midpoint, M, of line AB.
(d) Draw a line through the point M that is perpendicular to line AB.
▶️Answer/Explanation
(a) $46^{\circ}$
(b) $84$
(c) Mid-point marked $42$ mm along $AB$ from $A.$
(d) Line at $90^{\circ}$ to $AB$ at $M.$
(a) Measure the size of angle \( x \):
1. Use a protractor.
2. Place the midpoint of the protractor at point A.
3. Align the baseline with line AB.
4. Read the angle where line AC intersects the protractor scale.
(b) Measure the length of line AB:
1. Use a ruler, preferably one with millimeters for precision.
2. Place the ruler along line AB.
3. Record the length in millimeters.
(c) Mark the midpoint \( M \) of line AB:
1. Find the midpoint by dividing the length of AB by 2.
2. Mark this point M.
(d) Draw a line through point M that is perpendicular to AB:
1. Use a ruler and a set square.
2. Place the set square’s right angle at point M.
3. Draw a straight line through M, perpendicular to AB.
Question
Shade two more squares so that this pattern has rotational symmetry of order 2.
Answer/Explanation
Ans: 
Question
The lengths of each side of this triangle are the same.
(a) Write down the mathematical name for this triangle.
Answer/Explanation
Ans: Equilateral
(b) Write down the number of lines of symmetry for the triangle.
Answer/Explanation
Ans: 3
Question
(a) Write down the order of rotational symmetry of this shape.
(b) Draw the lines of symmetry on this shape.
Answer/Explanation
Ans:
(a) 2
(b) Both lines drawn
Question
Z E B R A
Write down the letters in the word above that have
(a) exactly one line of symmetry,
Answer/Explanation
Ans: E B A cao
(b) rotational symmetry of order 2.
Answer/Explanation
Ans: Z cao