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ABCD is a parallelogram. If m∠DAB = (5x)° and m∠DCB = (x + 52)°, what is the value of x?

1 Answer

Dec 8, 2017

$x = 13^{o}$ $x=13^o$

Explanation:

Opposite angles in a parallelogram are equal.

A proof of this if you wanted it is given [here.](https://mathbitsnotebook.com/Geometry/Quadrilaterals/QDThPf2.html)

Since $∠ D A B$ $/_DAB$ is opposite to $∠ D C B$ $/_DCB$ , this means:

$m ∠ D A B = m ∠ D C B$ $m/_DAB=m/_DCB$
$5 x = x + 52$ $5x=x+52$
$4 x = 52$ $4x=52$
$x = 13^{o}$ $x=13^o$

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