ABCD is a cyclic quadrilateral. AB and DC are produced to meet at P. AD and BC are produced to meet at Q.

If $\angle AQB=2x^\circ$ , $\angle QAB=3x^\circ$ and $\angle BPC=x^\circ$ , then what is the value of $x$ ?

Question

ABCD is a cyclic quadrilateral. AB and DC are produced to meet at P. AD and BC are produced to meet at Q.

If

\angle AQB=2x^\circ

,

\angle QAB=3x^\circ

and

\angle BPC=x^\circ

, then what is the value of

x

?

Accepted Answer

D - 20. In triangle QAB, angle ABC = 180 - 5x. Then angle PBC = 5x (exterior), and angle BCP = 180 - angle BCD = angle A = 3x (cyclic). Triangle PBC: x + 5x + 3x = 180, so x = 20. Check: A=60, B=80, C=120, D=100, which sums to 360.

Answer

A - 10

Answer

B - 24

Answer

C - 15

ABCD is a cyclic quadrilateral. AB and DC are produced to meet at P. AD and BC are produced to meet at Q. If \(\angle AQB=2x^\circ\), \(\angle QAB=3x^\circ\) and \(\angle BPC=x^\circ\), then what is…

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