Question

Please help me with #14 geometry

Answer 1

x = 19.5

Explanation:

#14

Given:

`\sf m\angle GFE = (6x+20)^\circ`

`\sf m\angle GFJ =(2x+4)^\circ`

To solve for x.

Solution:

By observing the figure, we can say that the angles are the angles in straight line.

since the sum of angle of straight line is equal to 180°.

So,

We can say that:

Given:

`\sf m\angle GFE +m\angle GFJ =180^\circ`

Substitute the value:

`\sf 6x+20+2x+4=180`

Simplify like terms:

`\sf 8x +24 =180`

Subtract 24 on both sides:

`\sf 8x = 180-24`

`\sf 8x =156`

Divide both sides by 8.

`\sf x =(156)/(8)`

`\sf x = 19.5`

Therefore, value of x is 19.5.

We can check our answer by substituting the value of x back into the original equations. If we substitute the value of x into the equation, we get:

`\sf m\angle GFE = (6x+20)^\circ = (6\cdot 19.5 +20)^\circ = 137^\circ`

`\sf m\angle GFJ =(2x+4)^\circ= (2\cdot 19.5 + 4)^\circ = 43^\circ`

The sum of these angles is 137 + 43= 180, which is indeed equal to 180°.

Therefore, the value of x is 19.5.