Part a: Option c: [tex]3x+90+x-14=180[/tex]
Part b: The value of x is 26
Explanation:
Part a:
Option a: [tex]3x+x-14=180[/tex]
Since, adding all the angles in the straight line results in 180°, and only two of the three angles were added in the equation to find the value of x.
Thus, the equation [tex]3x+x-14=180[/tex] cannot be used to determine the value of x.
Hence, Option a is not the correct answer.
Option b: [tex]3x+90+x-14=90[/tex]
Adding all the angles in the straight line results in 180°.
Thus, adding all the angles does not equals to 90°
Hence, the equation [tex]3x+90+x-14=90[/tex] cannot be used to determine the value of x.
Hence, option b is not the correct answer.
Option c: [tex]3x+90+x-14=180[/tex]
Since, the straight line is 180° and thus adding the angles in this straight line will result in 180°
Thus, the angles in this straight line are 3x, 90° and x-14.
Hence, adding these angles will result in 180°
Thus, the equation becomes
[tex]3x+90+x-14=180[/tex]
Hence, the equation used to determine the value of x is [tex]3x+90+x-14=180[/tex]
Thus, Option c is the correct answer.
Option d: [tex]4x+90=360[/tex]
Adding all the angles in the straight line results in 180°.
Since, not all the three angles were added in this equation and the equation equals to 180°
Hence, the equation [tex]4x+90=360[/tex] cannot be used to determine the value of x.
Thus, Option d is not the correct answer.
Part b:
To determine the value of x, we shall add all the angles of the equation [tex]3x+90+x-14=180[/tex]
Thus, we get,
[tex]4x+76=180[/tex]
Subtracting both sides by 76,
[tex]4x=104[/tex]
Dividing both sides by 4, we get,
[tex]x=26[/tex]
Thus, the value of x is 26.
