Question

Find the value of x.​ (Hint: The sum of the angle measures of a quadrilateral is 360degrees​.)
left parenthesis 4 x plus 40 right parenthesis degrees
3 x degrees
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Part 1
xequals
  
enter your response here ​(Simplify your​ answer.)

Answer 1

To find the value of \( x \), we can use the hint that the sum of the angle measures of a quadrilateral is \( 360^\circ \).

Let's define the angles in the quadrilateral based on the information you provided:

1. One angle is \( (4x + 40)^\circ \).
2. The second angle is \( 3x^\circ \).

Assuming there are two other angles (which are not specified), we can assume they are \( A \) and \( B \). However, since you only provided the expressions for two angles, let's set the sum of these two angles equal to \( 360^\circ \) first and solve for \( x \).

Let's assume the other two angles are zero or somehow not affecting the total for this current setting.

Now, we can write the equation:

\[
(4x + 40) + 3x = 360
\]

Combine like terms:

\[
4x + 3x + 40 = 360
\]

This simplifies to:

\[
7x + 40 = 360
\]

Now, subtract \( 40 \) from both sides:

\[
7x = 360 - 40
\]
\[
7x = 320
\]

Now, divide by \( 7 \):

\[
x = \frac{320}{7}
\]

Simplifying this gives:

\[
x \approx 45.71
\]

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

\[
x \approx 45.71
\]

Make sure to clarify if there are other angles or if additional information was omitted to ensure full accuracy in solving the quadrilateral's angle measures.