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Jika besar begin mathsize 14px style angle AOC equals 65 degree end style dan begin mathsize 14px style angle thin space BOD equals 140 degree end style, tentukan:

b. besar begin mathsize 14px style angle BEC end style

Jawaban:

Perhatikan perhitungan berikut.

Perhatikan bahwa begin mathsize 14px style angle AEC end style merupakan titik sudut dari dua tali busur yang berpotongan di dalam, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell angle AEC end cell equals cell 1 half times open parentheses angle AOC plus angle BOD close parentheses end cell row blank equals cell 1 half times open parentheses 65 degree plus 140 degree close parentheses end cell row blank equals cell 1 half times open parentheses 205 degree close parentheses end cell row blank equals cell 102 comma 5 degree end cell end table end style

Didapatkan begin mathsize 14px style angle AEC equals 102 comma 5 degree end style.

Perhatikan bahwa begin mathsize 14px style angle BEC end style dan begin mathsize 14px style angle AEC end style saling berpelurus, maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell angle BEC plus angle AEC end cell equals cell 180 degree end cell row cell angle BEC plus 102 comma 5 end cell equals cell 180 degree end cell row cell angle BEC end cell equals cell 180 degree minus 102 comma 5 degree end cell row cell angle BEC end cell equals cell 77 comma 5 degree end cell end table end style

Jadi, besar begin mathsize 14px style angle BEC end style adalah begin mathsize 14px style 77 comma 5 degree end style.

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