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Sum of Measures of Exterior Angles of a Polygon

A parallelogr...

Question

A parallelogram has two sides 60 m and 25 m and a diagonal 65 m long. Find z

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Solution

$H e r e x + 80^{o} = 180^{o} s i n c e t h e y a r e a d j a c e n n t a n g l e s o f a p a r a l l e l o g r a m . ⟹ x = 100^{o} . A g a i n t h e a n g l e o p p o s i t e t o x i s 80^{o} s i n c e t h e y a r e o p p o s i t e a n g l e s o f a p a r a l l e l o g r a m . F o r t h e s a m e r e a s o n y = 80^{o} . N o w t h e a n g l e o p p o s i t e t o x = 180^{o} - z (l i n e a r p a i r) ∴ 180^{o} - z = 80^{o} ⟹ z = 80^{o} A n s - x = 100^{o}, y = 80^{o}, z = 80^{o}$

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