for spreading the message "Save Girl Child Save Future" a rally was organized by some students of  a school. they were given a triangular cardboard piece PQR which they divided to three parts to make design and write slogan by drawing the angle bisector .PM of angle P and perpendicular  PN to base QR. prove that angle MNP=1/2(angleQ-angleR),where angleQ>angleR. what is the benefit of these type of rallies?
 
 

Asked by santhamma658 | 2nd Oct, 2015, 03:22: PM

Expert Answer:

begin mathsize 11px style It space should space be space the space angle space MPN space in space the space question. end style
begin mathsize 11px style In space right space angled space triangle space MPN comma space angle MPN equals 90 degree minus angle NMP... left parenthesis 1 right parenthesis angle NMP space is space the space external space angle space of space the space triangle space PMR. Hence comma space angle NMP equals angle straight R plus angle MPR... left parenthesis 2 right parenthesis From space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis comma space angle MPN equals 90 degree minus open parentheses angle straight R plus angle MPR close parentheses... left parenthesis 3 right parenthesis Since comma space PM space is space the space angle space bisector comma space angle MPR equals angle MPQ... left parenthesis 4 right parenthesis Also comma space angle MPQ equals angle MPN plus angle NPQ rightwards double arrow angle MPQ equals angle MPN plus open parentheses 90 degree minus angle straight Q close parentheses space open parentheses because triangle NPQ space is space straight a space right space triangle close parentheses rightwards double arrow angle MPR equals angle MPN plus open parentheses 90 degree minus angle straight Q close parentheses space open parentheses using space left parenthesis 4 right parenthesis close parentheses Using space the space above space value space of space angle MPR space in space left parenthesis 3 right parenthesis comma space we space get angle MPN equals 90 degree minus open parentheses angle straight R plus angle MPN plus open parentheses 90 degree minus angle straight Q close parentheses close parentheses rightwards double arrow angle MPN equals 90 degree minus angle straight R minus angle MPN minus 90 degree plus angle straight Q rightwards double arrow 2 angle MPN equals angle straight Q minus angle straight R rightwards double arrow angle MPN equals 1 half open parentheses angle straight Q minus angle straight R close parentheses space open parentheses Proved. close parentheses These space type space of space rallies space create space awareness space in space public space about space the space importance space of space gender space balance space in space the space world. end style

Answered by satyajit samal | 3rd Oct, 2015, 10:20: PM