two consecutive angles of a parallelogram are 160x and 260x respectively. name the parallelogram

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Solution

The consecutive angles of a parallelogram are 160x and 260x.
Suppose the angles of a parallelogram are $∠ A, ∠ B, ∠ C, ∠ D$

$N o w a s w e k n o w t h a t i n a p a r a l l e \log r a m, o p p o s i t e a n g l e s a r e e q u a l . H e n c e ∠ A = ∠ C = 160 x a n d ∠ B = ∠ D = 260 x N o w ∠ A + ∠ B + ∠ C + ∠ D = 360 ° (s u m o f t h e i n t e r i o r a n g l e s o f a p a r a l l e \log r a m i s 360 °) \Rightarrow 160 x + 160 x + 260 x + 260 x = 360 ° \Rightarrow 840 x = 360 ° \Rightarrow x = \frac{360 °}{840} = (\frac{3}{7}) ° H e n c e ∠ A = (\frac{3}{7}) ° \times 160 = (\frac{480}{7}) ° a n d ∠ B = (\frac{3}{7}) ° \times 260 = (\frac{780}{7}) ° N o w ∠ A + ∠ B = (\frac{480}{7}) ° + (\frac{780}{7}) ° = 180 ° S o t h e s u m o f c o n s e c u t i v e a n g l e s o f a p a r a l l e \log r a m i s 180 ° a n d t h e c o n s e c u t i v e a n g l e s a r e n o t e q u a l . H e n c e t h e p a r a l l e \log r a m i s a r h o m b u s$

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