In Fig. 16.205, chords AD and BC intersect each other at right angles at a point P. If ∠DAB=35°, then ∠ADC=

Question

In Fig. 16.205, chords AD and BC intersect each other at right angles at a point P. If &#x2220; DAB =35&#xB0;, then &#x2220; ADC =

Philoid · Accepted Answer

Given that,

Chords AD and BC intersect at right angles,

∠DAB = 35°

∠APC = 90°

∠APC + ∠CPD = 180°

90^o + ∠CPD = 180°

∠CPD = 90°

∠DAB = ∠PCD = 35° (Angles on the same segment)

In triangle PCD,

∠PCD + ∠PDC + ∠CPD = 180°

35° + ∠PDC + 90° = 180°

∠PDC = 45°

∠ADC = 45°