ICSE Class 9 Answered

$begin mathsize 12px style In space figure space ABCD space is space straight a space rhombus space in space which space the space diagram space DB space is space produced space to space straight E. space If space angle ABE equals 160 degree then space find space straight x comma straight y comma straight z ? end style$

Asked by Topperlearning User | 07 Aug, 2017, 09:00: AM

Expert Answer

$begin mathsize 12px style angle AOB equals straight z equals 90 degree space space space space space space open parentheses Diagonals space of space straight a space rhombus space bisect space each space other space at space right space angle close parentheses angle AOB equals 180 degree minus 160 degree space equals 20 degree In space increment space AOB comma angle BAO plus angle AOB plus angle ABO equals 180 degree angle BAO plus 90 degree plus 20 degree equals 180 degree angle BAO equals 70 degree Also comma space straight x equals angle BAO equals 70 degree space space space space open parentheses Alternate space interior space angles space are space equal space as space AB space parallel space to space CD close parentheses In space increment space ADB comma AD equals AB angle ABD equals angle ADB space space space space left parenthesis Angles space opposites space to space equal space sides space are space equal. right parenthesis straight y equals 20 degree end style$