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Question

In the given figure $C D ∥ E F$ and $A B$ is a transversal, and $∠ D G H = 2 x$ and $F H B = 5 x - 51$ degree.
Find the measure, in degrees, of $∠ B H E$

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Solution

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The darkened angles are corresponding and are congruent so we can set up the equation:

$2 x = 5 x - 51$

$- 3 x = - 51$

$x = \frac{51}{3}$

$x = 17$

Now, that we know the value of $x$ , we can determine the measure of the entire darkened angle:

angle's measurement $= 5 x - 51 = 5 (17) - 51 = 34$

$∠ B H E = 180 - 34 = 146$ (because they are supplementary)

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