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ICSE Class 10 Answered

ABCD is a cyclic quadrilateral with ADC = 135. Sides BA and CD produced meet at point P, sides AD and BC produced meet at point Q. If P:Q = 2:1, find angles P and Q.
Asked by bdroy_2014 | 25 Feb, 2018, 08:54: PM
answered-by-expert Expert Answer
 
begin mathsize 16px style Let space angle straight P equals 2 straight x comma space then space angle straight Q equals straight x Now comma space in space cyclic space quadrilateral space ABCD comma angle straight B equals 180 degree minus angle ADC equals 180 degree minus 135 degree equals 45 degree And comma space angle ADC plus angle ADP equals 180 degree space space space space space space left parenthesis linear space pair right parenthesis rightwards double arrow angle ADP equals 45 degree Now comma space in space triangle AQB comma angle straight A equals 180 degree minus left parenthesis 45 degree plus straight x right parenthesis equals 135 degree minus straight x space space space space space space space.... left parenthesis straight i right parenthesis In space triangle ADP comma Ext. space angle space straight A equals angle ADP plus angle straight P equals 45 degree plus 2 straight x space space space space space space space.... left parenthesis ii right parenthesis From space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma 45 degree plus 2 straight x equals 135 degree minus straight x rightwards double arrow 3 straight x equals 90 degree rightwards double arrow straight x equals 30 degree rightwards double arrow angle straight P equals 2 straight x equals 60 degree space and space angle straight Q equals straight x equals 30 degree end style
 
 
Answered by Rashmi Khot | 26 Feb, 2018, 11:40: AM

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