Two opposite angles of a parallelogram are (5x - 2) and (40

Opposite angles of a parallelogram are 3 x 2 and 50 x. Find the measure of each angle of the parallelogram.....

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Two adjecent angles of a parallelogram are (4x-1)and (5x+10) find the angles of a parallelogram

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Two adjecent angles of a parallelogram are (4x-1)and (5x+10) find the angles of a parallelogram

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Hint: We know that the opposite angles of a parallelogram are equal. So there are only 2 unique angles in a parallelogram. Here the two opposite angles, which are equal, are given and we have to solve for x and find the measure of these two opposite angles. Equate ${\left( {5x - 2} \right)^ \circ }$ and ${\left( {40 - x} \right)^ \circ }$to find the value of x.

Complete step-by-step answer:

We are given that the two opposite angles of a parallelogram are ${\left( {5x - 2} \right)^ \circ }$ and ${\left( {40 - x} \right)^ \circ }$We have to find the value of x.As we can see in the diagram, in a parallelogram opposite angles are equal. Given angles are opposite so they are equal that is why we must equate one with another.$5x - 2 = 40 - x$ Put all the x terms on the left hand side and all the constants on the right hand side.$ 5x + x = 40 + 2 \\ 6x = 42 \\ $ Divide 42 by 6 to get the value of x.$ x = \dfrac{{42}}{6} \\ x = 7 \\ $ Therefore, the value of x is 7.Then the measure of the given angles will be 33 degrees.$ 5x - 2 = 40 - x \\ 5\left( 7 \right) - 2 = 40 - 7 \\ 35 - 2 = 33 \\ 33 = 33 \\ $ Sum of interior angles of a parallelogram is 360 degrees.$ 33 + 33 + a + b = 360 \\ a = b \\ 66 + 2a = 360 \\ 2a = 360 - 66 \\ 2a = 294 \\ a = 147 \\ a = b = 147 \\ $ a=b because a and b are another set of opposite angles and are equal.The measures of angles of parallelogram in degrees are 33, 147, 33 and 147.

Note: A parallelogram is a quadrilateral. The opposite sides of a parallelogram are parallel and equal and the opposite angles of a parallelogram are equal. The diagonals of a parallelogram bisect each other.

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Two opposite angles of a parallelogram are (5x - 2) and (40 - x find the value of x)

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