Question

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Answer 1

Answer:

Step-by-step explanation:

Let the measures of the acute angle of the rhombus be x° and measure of obtuse angle be y° .

We know that,

the Sum of the adjacent angles of a rhombus is 180° .

Therefore,

x + y = 180 .................(i )

From the given condition we have,

y = 2x + 30

2x - y = -30 ........................( ii )

Adding equation (i ) and (ii ) we get

x + y = 180

2x-y = -30

----------------------------------------------------

3x = 150

x = 150/3

x = 50

Substituting the value of x in equation (i ) we get

x + y = 180

50 + y = 180

y = 180 - 50

y = 130

And we also know that,the opposite side and angles of a rhombus are the same.

Therefore, the measures of each angle of the rhombus is 50° ,130° ,50° and 130°

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