horselover66351 horselover66351
  • 25-05-2021
  • Mathematics
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Given parallelogram ABCD. If m∠ACD = (7x – 12)° and m∠BDC = (10x + 5)°, find x. Write your response in the form x=_____.

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erinna erinna
  • 28-05-2021

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].

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