Q) ABCD is a rhombus in which the altitude from D to side AB bisects AB.Then angle A and angle B, respectively are:
A) 60 degree , 120 degree
B) 120 degree , 60 degree
C) 80 degree , 100 degree
D) 100 degree , 80 degree

Asked by banerjee_milky | 19th Dec, 2016, 03:35: PM

Expert Answer:

 
 
begin mathsize 16px style In space increment AED space and space increment BED comma
DE equals DE space space space left parenthesis common right parenthesis
angle AED equals angle BED space space space space left parenthesis each space 90 degree right parenthesis
AE equals BE space left parenthesis given right parenthesis
rightwards double arrow increment AED space approximately equal to increment BED space left parenthesis SAS space congruence right parenthesis
rightwards double arrow AD equals BD space space space space left parenthesis CPCT right parenthesis
But comma space AD equals AB space left parenthesis sides space of space straight a space rhombus space are space equal right parenthesis
rightwards double arrow AD equals AB equals BD
rightwards double arrow increment ABD space is space an space equilateral space triangle.
rightwards double arrow angle straight A equals 60 degree
rightwards double arrow angle straight A equals angle straight C equals 60 degree space space left parenthesis opposite space angles space of space straight a space rhombus space aer space equal right parenthesis
Now comma space angle ABC plus angle BCD equals 180 degree space left parenthesis adjacent space angles space are space supplementary right parenthesis
rightwards double arrow angle ABC plus 60 degree equals 180 degree
rightwards double arrow angle ABC equals 120 degree
Now comma space angle ABC equals angle ADC equals 120 degree space space space space space left parenthesis opposite space angles space of space straight a space rhombus space are space equal right parenthesis
Thus comma space we space have
angle straight A equals 60 degree space and space angle straight B equals 120 degree end style

Answered by Rashmi Khot | 28th Nov, 2017, 02:22: PM