Answer:
The variable, y is 11°
Step-by-step explanation:
The given parameters are;
in triangle ΔABC; [tex]{}[/tex] in triangle ΔFGH;
Segment [tex]\overline {AB}[/tex] = 14 [tex]{}[/tex] Segment [tex]\overline {FG}[/tex] = 14
Segment [tex]\overline {BC}[/tex] = 27 [tex]{}[/tex] Segment [tex]\overline {GH}[/tex] = 19
Segment [tex]\overline {AC}[/tex] = 19 [tex]{}[/tex] Segment [tex]\overline {FH}[/tex] = 2·y + 5
∡A = 32° [tex]{}[/tex] ∡G = 32°
∡A = ∠BAC which is the angle formed by segments [tex]\overline {AB}[/tex] = 14 and [tex]\overline {AC}[/tex] = 19
Therefore, segment [tex]\overline {BC}[/tex] = 27, is the segment opposite to ∡A = 32°
Similarly, ∡G = ∠FGH which is the angle formed by segments [tex]\overline {FG}[/tex] = 14 and [tex]\overline {GH}[/tex] = 19
Therefore, segment [tex]\overline {FH}[/tex] = 2·y + 5, is the segment opposite to ∡A = 32° and triangle ΔABC ≅ ΔFGH by Side-Angle-Side congruency rule which gives;
[tex]\overline {FH}[/tex] ≅ [tex]\overline {BC}[/tex] by Congruent Parts of Congruent Triangles are Congruent (CPCTC)
∴ [tex]\overline {FH}[/tex] = [tex]\overline {BC}[/tex] = 27° y definition of congruency
[tex]\overline {FH}[/tex] = 2·y + 5 = 27° by transitive property
∴ 2·y + 5 = 27°
2·y = 27° - 5° = 22°
y = 22°/2 = 11°
The variable, y = 11°
