ABCD is a parallelogram, Calculate the size of angle x.
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reasons for your answer

Step-by-step explanation:

let point that BD intersects extended A be Z

angle BDA = 180 - 56 - 78 = 46 deg (supplementary angle in //ogram)

angle AZD = 180 - 98 = 82 deg (angles on a straight line/supplementary angles on straight line)

therefore,

angle x = 180 - 82 - 46 = 52 deg (sum angles of triangle)

yes

step-by-step explanation:

yes

< 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)