Final answer:
In this case, the value of x is approximately 23.857.
None of the given options is correct
Step-by-step explanation:
To find the value of x in the given problem, let's analyze the information provided.
We have an AVWX shape where VX is extended to point Y. We are given the measures of the angles VWX, ZXVW, and ZWXY in terms of x.
- 1. m VWX = (x + 14)°
- 2. m ZXVW = (x + 9)°
- 3. m ZWXY = (5x – 10)°
To find the value of x, we need to set up an equation using the given angles.
In AVWX, the sum of the angles is 360°. We can set up the equation:
m VWX + m ZXVW + m ZWXY + m XYW = 360°
Substituting the given values:
(x + 14) + (x + 9) + (5x – 10) + m XYW = 360°
Combining like terms:
7x + 13 + m XYW = 360°
Now, we need to find m XYW.
Since AVWX is a straight line, the sum of the angles VWX, ZXVW, and ZWXY should be equal to 180°.
Setting up the equation:
m VWX + m ZXVW + m ZWXY = 180°
Substituting the given values:
(x + 14) + (x + 9) + (5x – 10) = 180°
Combining like terms:
7x + 13 = 180°
Now, let's solve for x:
7x = 180° - 13
7x = 167°
x = 167° / 7
x ≈ 23.857
Therefore, the value of x is approximately 23.857.
None of the provided answer options (A, B, C, D) match the calculated value of x.