Determine the measure of the interior angle at vertex c.

120 degrees.

Step-by-step explanation:

This is a pentagon so the interior angles add up to 540 degrees, so we have:

4x + 4x + 4x + 3x + 3x = 540

18x = 540

x =  30 degrees.

So m < C = 4*30 = 120 degrees.

Angle at vertex C is equal to 120°

Step-by-step explanation:

First, we need to find the sum of its interior angle, the sum of the interior angle.

The sum of the interior angle of n-sided polygon is given as (n-2)180

Since in this case, we are dealing with a 5-sided polygon, then the sum of its interior angle will be (5-2)180=3 × 180=540

So, the sum of interior angle of a pentagon is 540

This implies; A + B + C + D + E = 540

                    3x + 4x + 4x + 4x + 3x = 540

                       18x = 540

Divide both-side of the equation by 18 to get the value of x

18x/18 = 540/18

x=30

angle at vertex C = 4x  =  4 ×  30  = 120

Therefore, angle at vertex C is equal to 120°

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180