Manhattan book gives an explanation that angle ABD= 180-2x

Why can we assume this is the case if we truly don’t know if line AC is straight? Why is angle ABD + angle CBD= 180?

Going further, why is line AB = line BD ???

Thanks

Manhattan book gives an explanation that angle ABD= 180-2x

Why can we assume this is the case if we truly don’t know if line AC is straight? Why is angle ABD + angle CBD= 180?

Going further, why is line AB = line BD ???

Thanks

In QC, you can assume, what looks to be a straight line to be a straight line. Thus AC is a straight line here.

u understood this right?

If yes, then in triangle ABD

Angle DAB + Angle ABD + Angle BDA=180

therefore, Angle DAB+ 180-2x + Angle BDA=180

Also, Angle DAB =x

so, x + 180-2x + Angle BDA=180

and finally, Angle BDA = 180 - 180 +2x - x

Angle BDA=x

since, Angle BDA = Angle DAB =x

line AB = BD by isosceles property of triangle

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