Given:
In the parallelogram ABCD, m∠ACD = (7x – 12)° and m∠BDC = (10x + 5)°.
To find:
The value of x.
Solution:
The diagonals of a parallelogram are perpendicular bisectors.
Let O be the intersection point of the diagonals.
In triangle OCD,
[tex]m\angle OCD+m\angle ODC+m\angle COD=180^\circ[/tex] [Angle sum property]
[tex](7x-12)+(10x+5)+90=180[/tex]
[tex]17x+83=180[/tex]
[tex]17x=180-83[/tex]
[tex]17x=97[/tex]
[tex]x=\dfrac{97}{17}[/tex]
Therefore, the value of x is equal to [tex]\dfrac{97}{17}[/tex].
