Pertanyaan

Titik sudut A,B,C dan D berada pada lingkaran. Jika besar ∠BAC = 28 o dan ∠AXD = 52 o , maka ∠DCX adalah ….

Titik sudut A,B,C dan D berada pada lingkaran. Jika besar ∠BAC = 28^o dan ∠AXD = 52^o, maka ∠DCX adalah ….

24^o
36^o
42^o
52^o

S. Dwi

Master Teacher

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Pembahasan

Perhatikan segitiga DXC!

$angle B D C space equals space angle B A C space equals space 28 to the power of o space space space space space space space angle A X D space equals space angle B X C space equals space 52 to the power of o space space space space space space left parenthesis S u d u t space b e r t o l a k space b e l a k a n g right parenthesis straight angle AXB equals straight angle DXC equals fraction numerator 360 to the power of o minus 52 to the power of o minus 52 to the power of o over denominator 2 end fraction equals 128 to the power of o$

Perhatikan segitiga DXC!

angle D X C plus angle X C D plus angle X D C equals 180 to the power of o 128 to the power of o plus angle X C D plus angle B D C equals 180 to the power of o 128 to the power of o plus angle X C D plus 28 to the power of o equals 180 to the power of o angle X C D plus 156 to the power of o equals 180 to the power of o angle X C D equals 24 to the power of o