(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) \(\stackrel\frown{ABC} = \frac{1}{2} \stackrel\frown{AOC} reflex\)
= \(\frac{1}{2} \times 190° = 95°\)
(ii) \(\stackrel\frown{ADC} = \frac{1}{2} \stackrel\frown{AOC}\)
= \(\frac{1}{2} (360° - 190°)\)
= \(\frac{1}{2} \times 170°\)
= 85°
(c) (i) \(\stackrel\frown{ABC} = \frac{360 - 190}{360} \times 2\pi r\)
= \(\frac{170}{360} \times 2 \times 3.142 \times 7\)
= \(20.77 cm\)
\(\approxeq 20.8 cm\) (3 significant figures)
(ii) \(AD = 2 \times 7\cos 35\)
= \(14 \times 0.8192\)
= \(11.468 cm \approxeq 11.5 cm\) (3 significant figures)