What is the measure of \blueD{\angle x}∠xstart color #11accd, angle, x, end color #11accd? Angles are not necessarily drawn to scale.

x = 71°

Step-by-step explanation:

By applying triangle sum theorem in ΔBHD,

m∠DBH + m∠BHD + m∠HDB = 180°

40° + m∠BHD + 31° = 180°

m∠BHD = 180° - 71° = 109°

m∠BHD + m∠DHE = 180° [Linear pair of angles]

109° + x° = 180°

x = 180° - 109°

x = 71°

< 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)

explanation:

step-by-step explanation: