Question

निम्न समांतर चतुर्भुजों में अज्ञात x, y, z के मानों को ज्ञात कीजिए:

Solution

(i) $angle straight y space equals space 100 degree$ [ समांतर चतुर्भुज के सम्मुख कोण बराबर होता हैं ]
समांतर चतुर्भुक्त के अंत:कोण का योग = $360 degree$
$straight x space plus space straight y space plus space straight z space plus space angle straight B space equals space 360 degree straight x space plus space 100 degree space straight z space plus space 100 degree space equals space 360 degree straight x space plus space straight z space equals space 360 degree space minus space 100 degree space minus space 100 degree equals space 160 degree straight x space equals space straight z straight x space equals space straight z space equals space fraction numerator 160 degree over denominator 2 end fraction space equals space 80 degree straight x space equals space 80 degree comma space space space straight z space equals space 80 degree comma space space straight y space equals space 100 degree$
(ii)
$angle 1 space equals space 50 degree space space space space space space space space space space space space space space space space space space space left square bracket space सम ् म ु ख space क ो ण space सम ा न space ह ो त े space ह ै space right square bracket angle 1 space plus space straight z space equals space 180 degree straight z space equals space 180 degree space minus space angle 1 straight z space equals space 180 degree space minus space 50 degree space equals space 130 degree straight x space plus space straight y space plus space 50 degree space plus space 50 degree space equals space 360 degree straight x space plus space straight y space equals space 360 degree space minus space 50 degree space minus space 50 degree straight x space plus space straight y space equals space 260 degree straight x space equals space straight y straight x space equals space straight y space equals space 260 over 2 space equals space 130 degree straight x space equals space 130 degree comma space space space straight y space equals space 130 degree comma space space space straight z space equals space 130 degree$
(iii) शीर्षाभिमुख कोण बराबर होते हैं
x = $90 degree$
त्रिभुज के कोणों का योग = $180 degree$
$90 degree space plus space 30 degree space straight y space equals space 180 degree straight y space equals space 180 degree space minus space 30 degree space minus space 90 degree space equals space 60 degree straight y space equals space straight z straight y space equals space 60 degree straight z space equals space 60 degree straight x space equals space 90 degree comma space space space straight y space equals space 60 degree comma space space space space straight z space equals space 60 degree$
(iv)