What is the measure of ∡ x in the figure below?For reference: In the figure shown P and Q are points of tangency and B C ⌢ + F E ⌢ = 130 o .. Calculate "x".

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What is the measure of   ∡  x in the figure below?For reference: In the figure shown P and Q are points of tangency and             B      C                      ⌢              +            F      E                      ⌢              =      130    o    .. Calculate &quot;x&quot;.

Branson Grimes · Accepted Answer

Step 1Let   ∡  P  Q  D  =  y.Thus,   2  y  +  x  =      180          ∘        ..Step 2In another hand, since ACDE is cyclic, we obtain:  y  +  x  +  ∡  C  D  B  +  ∡  F  D  E  =      180          ∘      or  y  +  x  +      65          ∘        =      180          ∘        ..Answer:   x  =      50          ∘        ..

tizamazg · Accepted Answer

Step 1Step 2  ∠  B  A  C  +  ∠  F  A  E  =      65    0    ∠  P  A  Q  =            ∠      P      O      Q        2    =      90    ∘    −      x    2    ∠  B  A  F  +  ∠  B  D  F  =      180    ∘      ⟹        65    ∘    +      90    ∘    −      x    2    +  x  =      180    ∘      ⟹    x  =      50    ∘

In the figure shown P and Q are points of tangency and hat{BC}+hat{FE}=130^circ. Calculate "x".

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