Question

Anyone know how to solve for x and y on this problem?

Answer 1

`\boxed{\boxed{\pink{\bf \dag Value \ of \ x \ is \ 6\ and\ y \ is\ (-21) .}}}`

Explanation:

In the Question , its given that ∆ART
`\cong` ∆ 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)

`\bf\implies AT = DI \\\\\bf\implies 6x + 31 = 67 \\\\\bf\implies 6x = 67 - 31 \\\\\bf\implies 6x = 36 \\\\\bf\implies x =(36)/(6)\\\\\bf\implies \boxed{\red{\bf x = 6}}`

Hence the value of x is 6 .

`\rule{200}2`

`\bf\implies AR = DF \\\\\bf\implies -4y+19 = 103\\\\\bf\implies -4y = 103-19 \\\\\bf\implies -4y = 84 \\\\\bf\implies y =(84)/(-4)\\\\\bf\implies \boxed{\red{\bf y = -21}}`

Hence the value of x is 6 and y is (-21) .