Question

Find the value of the variable.

Answer 1

Answer:

The variable, y is 11°

Step-by-step explanation:

The given parameters are;

in triangle ΔABC;          ${}$              in triangle ΔFGH;

Segment $\overline {AB}$ = 14         ${}$               Segment $\overline {FG}$ = 14

Segment $\overline {BC}$ = 27         ${}$              Segment $\overline {GH}$ = 19

Segment $\overline {AC}$ = 19         ${}$               Segment $\overline {FH}$ = 2·y + 5

∡A = 32°                       ${}$                ∡G = 32°

∡A = ∠BAC which is the angle formed by segments $\overline {AB}$ = 14 and $\overline {AC}$ = 19

Therefore, segment $\overline {BC}$ = 27, is the segment opposite to ∡A = 32°

Similarly, ∡G = ∠FGH which is the angle formed by segments $\overline {FG}$ = 14 and $\overline {GH}$ = 19

Therefore, segment $\overline {FH}$ = 2·y + 5, is the segment opposite to ∡A = 32° and triangle ΔABC ≅ ΔFGH by Side-Angle-Side congruency rule which gives;

$\overline {FH}$ ≅ $\overline {BC}$ by Congruent Parts of Congruent Triangles are Congruent (CPCTC)

∴ $\overline {FH}$ = $\overline {BC}$ = 27° y definition of congruency

$\overline {FH}$ = 2·y + 5 = 27° by transitive property

∴ 2·y + 5 = 27°

2·y = 27° - 5° = 22°

y = 22°/2 = 11°

The variable, y = 11°