What is the value of x? Enter your answer in the box. x = cm

What is the value of x? Enter your answer in the box. x = cm HELP PLEASE

Jan 26, 2018

$x = 5$

Explanation:

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The two triangles are similar by $\forall$ theorem because where the two lines cross there are two vertical angles, and vertical angles are congruent.

Additionally, there is another pair of angles that are shown in the figure to be congruent

Therefore, due to similarity, the ratio of corresponding sides are the same:

$\frac{32}{4} = \frac{40}{x}$

$32 x = 160$

$x = \frac{160}{32} = 5$