Determine the measure of the interior
angle at vertex E.

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°

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)