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2 years ago

Find the value of the variable.

Mathematics

1 answer:

nalin [4]2 years ago

8 0

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°

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Given:

Consider the expression are

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Solution:

1. We have,

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Answer:

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Step-by-step explanation:

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