in the figure given below a n is equal to AC angle BAC is equal to 52 degree angle is equal to 84 degree and BC came is a straight line prove that n b is equal to N C

In ANC, given AN=ACANC=ACN ...i   angles opposite to equal sides are equal.Now ,ANC+ACN+NAC=180°   angle sum property of 2ACN+52°=180°   using i and given NAC=52°2ACN=128°ACN=64°So, ANC=ACN=64°Now ACK+ACN+NCB=180°   Linear pair84°+64°+NCB=180°      givenACK=84° NCB=180°-148°NCB=32°Also, ANC+CNB=180°     Linear pair64°+CNB=180°CNB=116°Now consider NBCNBC+CNB+NCB=180°   angle sum property of NBC+116°+32°=180°NBC=180°-148°=32°Now NBC=NCB=32°NB=NC  sides opposite to equal angles are equal.Hence Proved.

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dfgyjh
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nb=nc because triangle nbc is a equilateral triangle and these triangles have three sides equal
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