(a)
In the diagram, AB // CD and BC // FE. (stackrelfrown{CDE} = 75°) and (stackrelfrown{DEF} = 26°). Find the angles marked x and y.
(b)
The diagram shows a circle ABCD with centre O and radius 7 cm. The reflex angle AOC = 190° and < DAO = 35°. Find :
(i) < ABC ; (ii) < ADC.
(c) Using the diagram in (b) above, calculate, correct to 3 significant figures, the length of : (i) arc ABC ; (ii) the chord AD. [Take (pi = 3.142)].
Explanation
(a) 105° + 26° + x = 180°
131° + x = 180°
x = 180° – 131°
= 49°.
131° + x + 131° + 360 – y = 360°
131° + 49° + 131° + 360 – y = 360°
671° – y = 360°
y = 671° – 360°
= 311°.
(b)(i) (stackrelfrown{ABC} = frac{1}{2} stackrelfrown{AOC} reflex)
= (frac{1}{2} times 190° = 95°)
(ii) (stackrelfrown{ADC} = frac{1}{2} stackrelfrown{AOC})
= (frac{1}{2} (360° – 190°))
= (frac{1}{2} times 170°)
= 85°
(c) (i) (stackrelfrown{ABC} = frac{360 – 190}{360} times 2pi r)
= (frac{170}{360} times 2 times 3.142 times 7)
= (20.77 cm)
(approxeq 20.8 cm) (3 significant figures)
(ii) (AD = 2 times 7cos 35)
= (14 times 0.8192)
= (11.468 cm approxeq 11.5 cm) (3 significant figures)