Lines AB and CD are parallel. If 7 measures (3x + 7)°, and 6 measures 76°, what is the value of x?

Measure of ∠6 = (3x + 7)°

Measure of ∠7 = 76°

∠6 and ∠7 are vertically opposite angles, so their measures will be equal.

Which means :

Let us now place 23 in the place of x and see if it forms 76 :

Thus, the value of x we found is correct.

Therefore, the value of x = 23

< 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)