Question

in the given figure if Angle B A D = 60 degree and angle ADC = 105 degree then determine angle DPC

Answer 1

Hi.

Here is your answer---

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Given---

∠ ADC = 105°

We know,
  ∠ADC + ∠ABC = 180°  [Opposite angles of the Cyclic Quadrilateral are                                                                             Supplementary]
   ∠ABC ( or ∠PBA) = 180° - 105°
                                = 75°
  
∠DAB( or ∠PAB) = 60° [Given]

Using the Angle Sum Property in ΔPAB,
 
             ∠PAB + ∠PBA + ∠APB = 180°
                    60° +  75° + ∠APB = 180°
                             ∠APB = 180° - 135°
                             ∠APB = 45°

Thus,  ∠DPC(or ∠APB) is 45°.

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Hope it helps.

Have a nice day.

Answer 2

Answer:

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