Pq and rs are two lines that intersect at point t. which fact is used to prove that angle pts is always equal to angle rtq?

a.) the sum of the measures of angles rtq and qts is equal to the sum of the measures of angles qts and pts.
b.) angle rtq and angle qts are complementary angles.
c.) the sum of the measures of angles rtq and pts is equal to the sum of the measures of angles rtp and qts.
d.) angle rtq and angle pts are supplementary angles.

Let PQ and RS be two lines that intersect at point T. Angles:

Subtract from first equation second equation:

As you can see, here you use option A - the sum of the measures of angles RTQ and QTS is equal to the sum of the measures of angles QTS and PTS.

correct choice is A.

the equivalent expression are always the hardest ones but you look at the gcf also

step-by-step explanation:

< 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)