A designer plans to create a new pattern of stitching a triangular piece of fabric shown in the figure above. She will stitch fabric in a straight line from the vertices of the triangle to the circumcenter of the triangle, located at point C, and then stitch an additional line of fabric back from the circumcenter to each vertex. How much fabric, in inches, will she need in total to create the design? (Note: Answer should be a whole number.)

54

Step-by-step explanation:

The circumcenter is the middle to each vertex. So since they gave you 9 in. and you have to go back and forth on each line, that is 18 in. per line. Considering there are three lines, add all of them together (Or multiple 18 by 3) to get 54 in.

Any other Prepworks questions? :)

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°