Question

Solve for x. Then, find m∠FDG and m∠GOF. A. x = 24; m∠FDG = 56°; m∠GOF = 106° B. x = 29; m∠FDG = 66°; m∠GOF = 126° C. x = 28; m∠FDG = 64°; m∠GOF = 116° D. x = 27; m∠FDG = 62°; m∠GOF = 118°

Answer 1

Option D

x = 27; m∠FDG = 62°; m∠GOF = 118°

Explanation:

To solve this, we will need the help of the following laws of geometry:

1. We can see that the shape formed is quadrilateral. The sum of the interior angles of a quadrilateral = 360 degrees.

2. The angle between a radius and a tangent = 90 degrees. as a result of this, <OGD = <OFD = 90 degrees.

Once we have values for all the angles of the quadrilateral, we can set up an equation using the first rule mentioned above.

2x+8 + 4x+10 +90 +90 = 360 (Sum of interior angles of a quadrilateral = 360)

6x = 162

x=27 degrees

Now we have the value of x, we can find FDG and GOF as follows:

FDG = 2x + 8 = 2(27)+8 =62

FOG = 4x + 10 = 4(27)+ 10 =118