Question

Answer part A and part B and explain how you got your answers please ❤️

Answer 1

Part a: Option c: $3x+90+x-14=180$

Part b: The value of x is 26

Explanation:

Part a:

Option a: $3x+x-14=180$

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 $3x+x-14=180$ cannot be used to determine the value of x.

Hence, Option a is not the correct answer.

Option b: $3x+90+x-14=90$

Adding all the angles in the straight line results in 180°.

Thus, adding all the angles does not equals to 90°

Hence, the equation $3x+90+x-14=90$ cannot be used to determine the value of x.

Hence, option b is not the correct answer.

Option c: $3x+90+x-14=180$

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

$3x+90+x-14=180$

Hence, the equation used to determine the value of x is $3x+90+x-14=180$

Thus, Option c is the correct answer.

Option d: $4x+90=360$

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 $4x+90=360$ 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 $3x+90+x-14=180$

Thus, we get,

$4x+76=180$

Subtracting both sides by 76,

$4x=104$

Dividing both sides by 4, we get,

$x=26$

Thus, the value of x is 26.