Question

Determine the measure of the interior angle at vertex C.

Answer 1

120 degrees.

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.

Answer 2

Angle at vertex C is equal to 120°

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°