iGCSE Mathematics (0580) - C4.6 Angles- Exam Style Questions Paper 3- New Syllabus
▶️ Answer/Explanation
(a)
An angle greater than $180^\circ$ and less than $360^\circ$ is a reflex angle.
✅ Answer: reflex
(b)
Sum the angles: $102 + 54 + 34 = 190^\circ$. This exceeds the sum of angles in a triangle.
✅ Answer: Angles in a triangle must add up to $180^\circ$.
(c)
First, find the interior angle BCD of the quadrilateral. The sum of angles in a quadrilateral is $360^\circ$.
$\text{Angle BCD} = 360^\circ – (126^\circ + 48^\circ + 75^\circ) = 360^\circ – 249^\circ = 111^\circ$
Since DCE is a straight line, angles on a straight line add to $180^\circ$.
$x = 180^\circ – 111^\circ = 69^\circ$
✅ Answer: $x = 69$
▶️ Answer/Explanation
(a)
Total interior angle sum $= (8 – 2) \times 180^\circ = 6 \times 180^\circ = 1080^\circ$
One interior angle = $\frac{1080^\circ}{8} = 135^\circ$
✅ Answer: $135^\circ$
(b)
The angle between a tangent and a radius (or diameter) is $90^\circ$. So, angle ABE = $90^\circ$ and angle ABD = $90^\circ$.
Since the whole angle from diameter AB to tangent BD is $90^\circ$, and angle ABC is given as $71^\circ$,
$x = 90^\circ – 71^\circ = 19^\circ$
✅ Answer: $x = 19$ because the angle between the tangent and radius is $90^\circ$.