Question

Find the supplement of the following angle:
${134}^{\circ }{30}^{{}^{\prime }}{26}^{\prime \prime }$ [2 MARKS]

Answer 1

Concept: 1 Mark
Application: 1 Mark

Supplement of an angle of ${134}^{\circ }{30}^{{}^{\prime }}{26}^{\prime \prime }$

$={180}^{\circ }–\left({134}^{\circ }{30}^{{}^{\prime }}{26}^{\prime \prime }\right)$

$=({179}^{\circ }+1^{\circ })-({134}^{\circ }+{30}^{{}^{\prime }}{26}^{\prime \prime })$

$=({179}^{\circ }–{134}^{\circ })+(1^{\circ }–{30}^{{}^{\prime }}{26}^{\prime \prime })$

$={45}^{\circ }+({60}^{{}^{\prime }}–({30}^{{}^{\prime }}+{26}^{\prime \prime }\left)\right)[1^{\circ }={60}^{{}^{\prime }}]$

$={45}^{\circ }+({59}^{{}^{\prime }}+1^{{}^{\prime }})–({30}^{{}^{\prime }}+{26}^{\prime \prime })\left)\right[1^{\circ }={60}^{{}^{\prime }}]$

$={45}^{\circ }+({59}^{{}^{\prime }}–{30}^{{}^{\prime }})+(1^{{}^{\prime }}–{26}^{\prime \prime })[1^{{}^{\prime }}={60}^{\prime \prime }]$

$={45}^{\circ }+{29}^{{}^{\prime }}+{34}^{\prime \prime }$

$={45}^{\circ }{29}^{{}^{\prime }}{34}^{\prime \prime }$