Geometry Topic Question [Edexcel Mathematics B (4MB1) 2014-2016]

1	(Edexcel/Math B/2014/jan/paper01/q4) In the diagram, \(\triangle ABC\) is an isosceles triangle with \(AB = AC\) and \(\angle BAC = 70^\circ\).  Given that \(ACD\) is a straight line, calculate the size, in degrees, of \(\angle BCD\). [2]
	(Edexcel/Math B/2014/jan/paper01R/q1) In triangle \(ABC\), \(\angle ABC = 56^\circ\).  The point \(D\) on \(AB\), and the point \(E\) on \(BC\), are such that \(DE\) is parallel to \(AC\).  \(\angle BDE = 52^\circ\) and \(\angle EAC = 34^\circ\).  Find the size of  (a) \(\angle DAE\), [1]  (b) \(\angle AEC\). [1]
3	(Edexcel/Math B/2014/jan/paper01R/q18) The sum of the interior angles of a regular polygon is \(2340^\circ\).  Calculate the size, in degrees, of an exterior angle of this polygon.[4]
4	(Edexcel/Math B/2014/june/paper01/q4) Calculate the size, in degrees, of an exterior angle of a 24-sided regular polygon.[2]
5	(Edexcel/Math B/2014/june/paper01R/q1) In the diagram, the four straight lines meet at a point. Find the value of \(x\).[2]
6	(Edexcel/Math B/2015/jan/paper01/q4) The diagram shows a regular octagon with three diagonals drawn.  Write down  (a) the number of lines of symmetry of the diagram,[1]  (b) the order of rotational symmetry of the diagram.[1]
7	(Edexcel/Math B/2015/jan/paper01/q21) \(ABCDEF\) is a regular hexagon.  Calculate, in degrees, the size of  (a) \(\angle ABC\),[2]  (b) \(\angle DAE\).[3]
8	(Edexcel/Math B/2015/jan/paper01R/q14) Each interior angle of a regular polygon is \(150^\circ\). Calculate the number of sides of the polygon.[3]
9	(Edexcel/Math B/2015/june/paper01/q14) \(ABC\) is an isosceles triangle with \(AB = AC = 12 \, \text{cm}\) and \(\angle BAC = 42^\circ\).  Calculate the length, in cm, of the third side of the triangle.[3]
10	(Edexcel/Math B/2016/jan/paper01/q16) (a) Write down the order of rotational symmetry of a regular octagon.[1]  The sum of the interior angles of a regular polygon is \(900^\circ\).  (b) Find the number of sides of this polygon.[2]
	to be continued...

 Geometry Answer Key

1.   $\angle B C D=125  $
2.   (a) $18^{\circ}$ (b) $(56+18) \quad$
3.   $ 24 \quad$
4.   $ 15^{\circ} \quad$
5.   $ x=42$
6.   (a) $2 \quad$ (b) $2 \quad $
7.   (a) $120^\circ$ (b) $30^\circ$
8.   $12$
9.   $8 .60(\mathrm{~cm})$
10.   (b) no of sides $=7$
11.   (a) diagram (b) diagram (c) diagram
12.   (a) 3 (b) 3 
13.   (a) $40^{\circ}$ (b) $5.22(\mathrm{~m})$ (c) $18.1\left(\mathrm{~cm}^2\right) \quad$
14.   $n=13$
15.   $\angle B A C=10^{\circ}$
16.   $\angle O A B=30^{\circ}$
17.   $ C X=x=3, X E=6 \mathrm{~cm}$ 
18.   (a) $50^{\circ}$ (b) $65^{\circ}$ (c) $35^{\circ} \quad$
19.   $ \angle C O D=40^{\circ} $
20.   (a) $x=24$ (b) $y=31$
21.   (a) $F B=24$ (b) $r=10 \quad $
22.   Show
23.   (a) $D A=72 \mathrm{~cm}$ (b) $A C=39.8 \mathrm{~cm}$, radius $=19.9 \mathrm{~cm} \quad$
24.   $16^{\circ} \quad $
25.   (a) $10 \mathrm{~cm}$ (b) $A E=5 \mathrm{~cm}$ (c) $A B=3 \mathrm{~cm}$ (d) $7.16 \mathrm{~cm}$
26.   (a) $E C=16.2(\mathrm{~cm})$ (b)$ 9.24$, $9.37 \rightarrow 9.41 \quad$ (c) $12.9 \rightarrow 13.2 \quad$
27.   (a) $\angle C D A=62^{\circ} \quad$ (b) $\angle C B A=118$
28.   radius $=6 \mathrm{~cm} \quad$
29.   (a) show (b) Explain
30.   (a) 7 (b) 19
31.   (a) $50^\circ$ (b) $\angle BAD = 95, \angle BCD = 85$ (c) $\angle QDA=130, \angle DEA=130$
32.   (a) $E F=10.0 \mathrm{~cm} \quad$ (b) show  (c) $E B=3.38$
33.   (a)(i) $80^{\circ} \quad$ (ii) $62^{\circ}$ (b) show (c) $34^{\circ} \quad$
34.   $A X=12 \mathrm{~cm}$
35.   (a) S Labelled (b) $T$ labelled (c)(i) $306^{\circ}\left( \pm 3^{\circ}\right)$ (ii) 9 or $10 \mathrm{~km}$
36.   (a) diagram (b) diagram (c) $ 9.1 \mathrm{~cm}( \pm 0.1) $
37.   (a) diagram (b) diagram (c) diagram 
38.   Diagram
39.   (a) Diagram (b) $4 .3( \pm 0.1) \mathrm{cm}$
40.   (a) Diagram (b) diagran (c) $22.6 \mathrm{~km}( \pm 0.5 \mathrm{~km}$ $=(\mathrm{1 mm}) $
41.   (a) diagram (b) diagram (c) $6.9( \pm 0.2) \mathrm{cm}$ (d) region shaded
42.   (a) Diagram (b) diagram
43.   (a) Diagram (b) Diagram (c) $\angle A P M=55( \pm 1)^{\circ}$