Question

Find the value of each variable in the parallelogram.18(b + 16)°F103°a - 10

Answer 1

The figure in the picture is a parallelogram, to calculate the variables "a" and "b" you have to keep in mind the properties of this shape, which are:

• The opposite sides are congruent

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• The opposite angles are congruent

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• The diagonals bisect the shape into two congruent triangles

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• The diagonals bisect each other

Considering the first property mentioned above, since the opposite sides are equal, then we know that:

`a-10=18`

From this expression we can determine the value of "a", what you have to do is pass "-10" to the right side of the equal sign. To pass the value from one side to the other you have to apply the opposite operation "+10" to both sides of the expression.

`\begin{gathered} a-10+10=18+10 \\ a=28 \end{gathered}`

So the value of "a" is 18

To determine the value of "b" we can apply the second property mentioned above, which is that the opposite angles of a parallelogram are congruent so that:

`b+16=103`

Using this expression we can calculate the value of "b", you have to pass "+16" to the right side of the equation by applying the opposite operation "-16" to both sides of it:

`\begin{gathered} b+16-16=103-16 \\ b=87 \end{gathered}`

The value of "b" is 87