What is the mode of 156 157 158 159 160 161 162 163 164 165

There is no mode in this sequence.

Step-by-step explanation:

The mode is the most frequent number.

In your case, we can analyze the set:

156, 157, 158, 159, 160, 161, 162, 163, 164, 165

Since these are all straightforward consecutive integers, there are no recurring numbers.

Thus, there is no mode in this sequence.

b and c

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)