Please provide solution to Part (ii) of the above question

Asked by saif | 22nd Mar, 2017, 12:47: AM

Expert Answer:

begin mathsize 16px style left parenthesis straight i right parenthesis space Given space that space ABCD space is space straight a space square space and space DEC space is space an space equilateral space triangle.
So comma space AB equals BC equals AD equals DC
and space DC equals EC equals DE
rightwards double arrow AB equals BC equals AD equals DC equals EC equals DE
In space increment ADE comma
AD equals DE
rightwards double arrow angle DAE equals angle DEA space.... left parenthesis straight i right parenthesis
Similarly comma space EC equals BC
rightwards double arrow angle CEB equals angle CBE space space.... left parenthesis ii right parenthesis
Looking space at space the space figure comma space we space can space see space that space we space are space given space
angle DEA equals angle CEB space space..... left parenthesis iii right parenthesis
Now comma space angle EAB equals 90 degree minus angle DAE space space and space angle EBA equals 90 degree minus angle CBE
rightwards double arrow angle EAB equals angle EBA space.... left parenthesis From space left parenthesis straight i right parenthesis comma space left parenthesis ii right parenthesis space and space left parenthesis iii right parenthesis right parenthesis
rightwards double arrow AE equals BE
Hence space proved.

left parenthesis ii right parenthesis space In space increment DAE comma
angle DEA plus angle DAE plus angle ADE equals 180 degree
rightwards double arrow angle DEA plus angle DAE plus left parenthesis angle ADC plus angle CDE right parenthesis equals 180 degree
rightwards double arrow angle DAE plus angle DAE plus left parenthesis 90 degree plus 60 degree right parenthesis equals 180 degree
space space space space space space space space space space space space... left parenthesis Since space angles space of space straight a space square space are space 90 degree space and space angles space of space an space equilateral space triangle space are space 60 degree right parenthesis
rightwards double arrow 2 angle DAE equals 30 degree
rightwards double arrow angle DAE equals fraction numerator 30 degree over denominator 2 end fraction equals 15 degree

end stylebegin mathsize 16px style left parenthesis straight i right parenthesis space Given space that space ABCD space is space straight a space square space and space DEC space is space an space equilateral space triangle.
So comma space AB equals BC equals AD equals DC
and space DC equals EC equals DE
rightwards double arrow AB equals BC equals AD equals DC equals EC equals DE
In space increment ADE comma
AD equals DE
rightwards double arrow angle DAE equals angle DEA space.... left parenthesis straight i right parenthesis
Similarly comma space EC equals BC
rightwards double arrow angle CEB equals angle CBE space space.... left parenthesis ii right parenthesis
Looking space at space the space figure comma space we space can space see space that space we space are space given space
angle DEA equals angle CEB space space..... left parenthesis iii right parenthesis
Now comma space angle EAB equals 90 degree minus angle DAE space space and space angle EBA equals 90 degree minus angle CBE
rightwards double arrow angle EAB equals angle EBA space.... left parenthesis From space left parenthesis straight i right parenthesis comma space left parenthesis ii right parenthesis space and space left parenthesis iii right parenthesis right parenthesis
rightwards double arrow AE equals BE
Hence space proved.

left parenthesis ii right parenthesis space In space increment DAE comma
angle DEA plus angle DAE plus angle ADE equals 180 degree
rightwards double arrow angle DEA plus angle DAE plus left parenthesis angle ADC plus angle CDE right parenthesis equals 180 degree
rightwards double arrow angle DAE plus angle DAE plus left parenthesis 90 degree plus 60 degree right parenthesis equals 180 degree
space space space space space space space space space space space space... left parenthesis Since space angles space of space straight a space square space are space 90 degree space and space angles space of space an space equilateral space triangle space are space 60 degree right parenthesis
rightwards double arrow 2 angle DAE equals 30 degree
rightwards double arrow angle DAE equals fraction numerator 30 degree over denominator 2 end fraction equals 15 degree

end style

Answered by Rebecca Fernandes | 22nd Mar, 2017, 09:00: AM