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CBSE Class 9 Answered

In the  given figure, find the measure of angle ABD , PDA , CAB and CBD ?
Asked by nisha_vini29 | 10 Feb, 2016, 11:30: AM
answered-by-expert Expert Answer
begin mathsize 14px style In space the space given space figure comma angle FDE space equals space 75 degree space space space therefore angle ADC space equals space 75 degree space space space... left parenthesis Opposite space angles right parenthesis In space increment ADC comma space angle straight C space equals 55 degree space space... left parenthesis Given right parenthesis angle straight D space equals space 75 degree space space... left parenthesis Given right parenthesis therefore angle straight A equals 180 minus open parentheses 55 plus 75 close parentheses equals 180 minus 130 space equals space 50 degree space space... space left parenthesis 1 right parenthesis Now comma space angle straight x equals 180 minus open parentheses 55 plus 90 close parentheses equals 180 minus 145 space equals space 35 degree space space... space left parenthesis 2 right parenthesis therefore angle straight a space equals space 35 degree.. left parenthesis Angle space subtended space by space the space same space arc right parenthesis therefore angle straight y equals 75 space minus space 35 space equals space 40 degree space space... space left parenthesis 3 right parenthesis space Hence comma space angle straight z equals 40 degree space space... left parenthesis Angle space subtended space by space the space same space arc right parenthesis space space space... space left parenthesis 4 right parenthesis straight i. space angle ABD In space increment ABD comma space angle straight A space equals open parentheses 50 degree plus 40 degree close parentheses space equals space 90 degree comma space space angle straight D space equals 35 degree space space space... space left parenthesis 2 right parenthesis therefore angle straight B equals 180 minus open parentheses 90 plus 35 close parentheses equals 180 minus 125 space equals 55 degree space therefore angle ABD space equals 55 degree space space ii. space angle PDA space equals angle straight x space equals 35 degree space space space... space left parenthesis 2 right parenthesis iii. angle CAB space equals angle straight z equals 40 degree space space space... space left parenthesis 4 right parenthesis iv. angle CBD space equals space 105 space minus angle ABD therefore angle CBD space equals space 105 space minus 55 space equals 50 degree space   end style
 
 

Answered by Priti Shah | 10 Feb, 2016, 06:30: PM
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