PQ and RS are two lines that intersect at point T, as shown below: Two lines PQ and RS intersect at point T. Angles PTS and RTQ are shown congruent.

Which fact is used to prove that angle PTS is always equal to angle RTQ? (1 point)

Sum of the measures of angles RTQ and QTS is 180°.
Lines PQ and RS intersect at an angle greater than a right angle.
Line segments PQ and RS do not have a fixed length.
Sum of the measures of angles PTR and QTS is 180°.

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< 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)