Question

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Part 1
Find the value of x.​ (Hint: The sum of the angle measures of a quadrilateral is 360degrees​.)
left parenthesis 5 x plus 45 right parenthesis degrees
4 x degrees
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Part 1
xequals
  
enter your response here ​(Simplify your​ answer.)

Answer 1

To find the value of \( x \) in a quadrilateral where the angle measures are given, we can set up the equation based on the sum of the angles in a quadrilateral, which equals \( 360^\circ \).

The given angles are:
1. \( 5x + 45 \) degrees
2. \( 4x \) degrees

We can express the sum of these angles as:

\[
(5x + 45) + 4x = 360
\]

Now, simplify the left side of the equation:

\[
5x + 45 + 4x = 360
\]
\[
9x + 45 = 360
\]

Next, isolate \( x \) by subtracting 45 from both sides:

\[
9x = 360 - 45
\]
\[
9x = 315
\]

Now, divide both sides by 9:

\[
x = \frac{315}{9}
\]

Simplify \( \frac{315}{9} \):

\[
x = 35
\]

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

\[
\boxed{35}
\]