In Fig. 16.195, ABCD is a cyclic quadrilateral in which ∠ BAD =75°, ∠ ABD =58° and ∠ ADC =77°, AC and BD intersect at P. Then, find ∠ DPC .

Question

In Fig. 16.195, ABCD is a cyclic quadrilateral in which &#x2220; BAD =75&#xB0;, &#x2220; ABD =58&#xB0; and &#x2220; ADC =77&#xB0;, AC and BD intersect at P. Then, find &#x2220; DPC .

Philoid · Accepted 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. 16.195, ABCD is a cyclic quadrilateral in which ∠BAD=75°, ∠ABD=58° and ∠ADC=77°, AC and BD intersect at P. Then, find ∠DPC.