Challenge  The measure of angleABD is left parenthesis 0.19 x plus 58 right parenthesis degrees and the measure of angleCBD is left parenthesis 0.06 x plus 37 right parenthesis degrees. Find the value of x.

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Part 1
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1 answer

To find the value of \( x \), we first need to understand the relationship between angles \( \angle ABD \) and \( \angle CBD \). Assuming that points A, B, C, and D are positioned such that angles \( ABD \) and \( CBD \) are adjacent and form a linear pair (meaning they are supplementary), we can write the equation:

\[ \angle ABD + \angle CBD = 180^\circ \]

Substituting the expressions for the angles, we get:

\[ (0.19x + 58) + (0.06x + 37) = 180 \]

Now, we can combine like terms:

\[ 0.19x + 0.06x + 58 + 37 = 180 \]

This simplifies to:

\[ 0.25x + 95 = 180 \]

Next, we isolate \( x \) by subtracting 95 from both sides:

\[ 0.25x = 180 - 95 \]

\[ 0.25x = 85 \]

Now, divide both sides by 0.25 to solve for \( x \):

\[ x = \frac{85}{0.25} \]

\[ x = 340 \]

Thus, the value of \( x \) is:

\[ \boxed{340} \]