Answer:
[tex]\boxed{\boxed{\pink{\bf \dag Value \ of \ x \ is \ 6\ and\ y \ is\ (-21) .}}}[/tex]
Step-by-step explanation:
In the Question , its given that ∆ART [tex]\cong[/tex] ∆ DFI . And we need to find the values of x and y . So we know that ,
- If two triangles are congruent then their Corresponding angles and sides are equal.
Hence here in ∆ ART & ∆ DFI :-
- AT = DI ( cpctc)
- AR = DF ( cpctc)
[tex]\bf\implies AT = DI \\\\\bf\implies 6x + 31 = 67 \\\\\bf\implies 6x = 67 - 31 \\\\\bf\implies 6x = 36 \\\\\bf\implies x =\dfrac{36}{6}\\\\\bf\implies \boxed{\red{\bf x = 6}}[/tex]
Hence the value of x is 6 .
[tex]\rule{200}2[/tex]
[tex]\bf\implies AR = DF \\\\\bf\implies -4y+19 = 103\\\\\bf\implies -4y = 103-19 \\\\\bf\implies -4y = 84 \\\\\bf\implies y =\dfrac{84}{-4}\\\\\bf\implies \boxed{\red{\bf y = -21}}[/tex]
Hence the value of x is 6 and y is (-21) .
