Understanding Engineering Mathematics

Solution to review question 5.1.10

(i) In Figure 5.9(i) we haveBAD+ BCD= 180 °=a+ 125 °.Soa=

55 °by supplementary angles in a cyclic quadrilateral. By angles on a

line,d= 180 °− 95 °= 85 °. Then by supplementary anglesABC=

180 −d= 95 °and angles on a line givesb= 180 °− 95 °= 85 °.

(ii) In Figure 5.9(ii) opposite angles in a cyclic quadrilateral gives

a+ 3 a= 4 a= 180 °

Soa= 45 °.Thenb= 2 a= 90 °.

5.3 Reinforcement

5.3.1 Division of a line in a given ratio

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A.The lineAB is 4 cm long.P is a point which dividesAB internally in the ratio
AP:PB=p:qfor the values of p and q given below. In each case determine the
lengthsAP,PB. Repeat the exercise when the division is external, in the same ratios.
Leave your answers as fractions in simplest form.

(i) 2 : 1 (ii) 3 : 2 (iii) 5 : 4 (iv) 3 : 7 (v) 1 : 5

B.With the same ratios as in QuestionA, it is given thatAP=2 cm. DeterminePB

andABin each case.

5.3.2 Intersecting and parallel lines and angular measurement

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Fill in all remaining angles:

(i) (ii)

130 °

80 °

5.3.3 Triangles and their elementary properties

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A.In each case the pairs of angles are angles in a triangle. Determine the other angle,

and the corresponding external angle.

(i) 32°,45° (ii) 73°,21° (iii) 15°,21° (iv) 85°,65°