The ratio of two supplementary angles is 4: 5. find the measures of each angle.

80

100

Step-by-step explanation:

Let the multiplier = x

4x + 5x = 180                     Combine the left

9x = 180                             Divide by 9

9x/9 = 180/9

x = 20                                 Use x to find the two angles

4x = 4 * 20 = 80              

5x = 5 * 20 = 100

The two angles are 80 and 100 which is 80/100 = 4//5

< 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)