Question

in the figure below AN=AC, angle BAC=52 degree, angle ACK=84 degree and BCK is a straight line .prove that NB =NC
whoever will give me the right answer I will mark Brainliest . ​

Answer 1

Step-by-step explanation:

triangle NAC is an isosceles triangle because NA=AC

therefore angle ACN = angle ANC= x

x+x+52°=180° (angle sum property)

2x=180°-52°

x=128°/2=64°

angle ANC = angle ACN = 64°

Now, let angle ABC be y and angle NCB be z

Now,

angle BNC + angle ANC = 180° (straight line)

angle BNC + 64° = 180°

angle BNC = 180°- 64° = 116°

now,

angle ACK + angle ACN + angle BCN = 180° (straight line)

angle BCN + 84° + 64° = 180°

angle BCN = 180°- 148° = 32°

Now,

angle NBC + angle BCN + angle BNC = 180° (angle sum property)

angle NBC + 32° + 116°= 180°

angle NBC = 180° - 148°=32°

Hence NB = NC because equal and opposite angles have equal and opposite sides

Hope this helps you