Re: M04, Q7

If quadrilateral \(ABCD\) is inscribed into a circle, what is the value of \(\angle BAD\) ?

1. \(AC = CD\)
2. \(\angle ADC = 70^\circ\)


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Explanation:

If ABCD is a quadrilateral then:

total of all angle's is 360.

Now, in stmt 1 they are saying that AC (which could be the diameter of the circle) = CD (one of the sides of the quad)
- This helps us in understanding that angle ADC = angle DAC = x
and that x + x + angle ACD = 180
and that angle ACD = 180 - 2x
What we need is angel BAD which is not provided in Stmt 1, thus NS

Stmt 2
gives angel ADC = 70 deg
which does not help us in estimating any other angle since a quadrilateral can be a square, parallelogram or a rhombus so angles can be different

Combining stmt 1 and stmt 2 we get
angle ADC = 70 deg = angle CAD
But we are still missing information about the other angle's i.e.
angle ABC + angle BCD + angle ADC + angle BAD = 360
angle ABC + angle BCD + angle 70 + (angle BAC + angle CAD) = 360
angle ABC + angle BCD + angle 70 + (angle BAC + 70) = 360

Rest of the angles above are still missing. Thus, E
If we were told what kind of a quad it is then it would be easier to find out the angle.