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ICSE Class 9 Answered

In the figure, AB is parallel to DC, angle BCE = 80 and angle BAC = 25. Find (i) angle CAD (ii) angle CBD (iii) angle ADC
Asked by pereiracalida | 17 Jan, 2018, 10:47: PM
Expert Answer
begin mathsize 16px style angle ABC equals angle BCE equals 80 degree space space space left parenthesis AB parallel to DC comma space alternate space angles right parenthesis angle ACD equals angle BAC equals 25 degree space space space left parenthesis AB parallel to DC comma space alternate space angles right parenthesis In space triangle ABC comma angle CAB plus angle ABC plus angle BCA equals 180 degree rightwards double arrow 25 degree plus 80 degree plus angle BCA equals 180 degree rightwards double arrow angle BCA equals 75 degree angle DAB plus angle DCB equals 180 degree space space left parenthesis opposite space angles space of space cyclic space quad. space are space supplementary right parenthesis rightwards double arrow left parenthesis angle CAD plus angle CAB right parenthesis plus left parenthesis angle ACD plus angle BCA right parenthesis equals 180 degree rightwards double arrow left parenthesis angle CAD plus 25 degree right parenthesis plus left parenthesis 25 degree plus 75 degree right parenthesis equals 180 degree rightwards double arrow angle CAD equals 55 degree Now comma space angle CBD equals angle CAD space space space left parenthesis angles space in space the space same space segment right parenthesis rightwards double arrow angle CBD equals 55 degree angle ADC plus angle ABC equals 180 degree space space space space left parenthesis opposite space angles space of space cyclic space quad. space are space supplementary right parenthesis rightwards double arrow angle ADC plus 80 degree equals 180 degree rightwards double arrow angle ADC equals 100 degree end style
Answered by Rashmi Khot | 18 Jan, 2018, 11:43: AM

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