In Fig. ABCD is a cyclic quadrilateral in which ∠BAD = 75°, ∠ABD

1.	In Fig. ABCD is a cyclic quadrilateral in which ∠BAD = 75°, ∠ABD = 58° and ∠ADC = 77°, AC and BD intersect at P. Then, find ∠DPC.
Answer» ∠DBA = ∠DCA = 58° (Angles on the same segment) In triangle DCA, ∠DCA + ∠CDA + ∠DAC = 180° 58° + 77° + ∠DAC = 180° ∠DAC = 45° ∠DPC = 180° - 58° - 30° = 92°

In Fig. ABCD is a cyclic quadrilateral in which ∠BAD = 75°, ∠ABD = 58° and ∠ADC = 77°, AC and BD intersect at P. Then, find ∠DPC.

Answer»

∠DBA = ∠DCA = 58°

(Angles on the same segment)

In triangle DCA,

∠DCA + ∠CDA + ∠DAC = 180°

58° + 77° + ∠DAC = 180°

∠DAC = 45°

∠DPC = 180° - 58° - 30°

= 92°

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In Fig. ABCD is a cyclic quadrilateral in which ∠BAD = 75°, ∠ABD = 58° and ∠ADC = 77°, AC and BD intersect at P. Then, find ∠DPC.

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