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
,
• The opposite angles are congruent
,
• The diagonals bisect the shape into two congruent triangles
,
• The diagonals bisect each other
Considering the first property mentioned above, since the opposite sides are equal, then we know that:
[tex]a-10=18[/tex]
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.
[tex]\begin{gathered} a-10+10=18+10 \\ a=28 \end{gathered}[/tex]
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:
[tex]b+16=103[/tex]
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:
[tex]\begin{gathered} b+16-16=103-16 \\ b=87 \end{gathered}[/tex]
The value of "b" is 87
