Find the value of x. The diagram is not to scale. Given RS = ST, m RST = 7x - 54, mSTU = 8x

Solution:

Given,

RS = ST

m RST = 7x - 54

mSTU = 8x

In the above question, the triangle has two same sides RS = ST.

That means the angle R is the same as T.

RST = 7x - 54

If STU = 8x then T = R = 180 - 8X

Adding all 3 angles of the triangle, we get,

R + S + T = 180

7x - 54 + 180 - 8x + 180 - 8x = 180

7x + 360 - 16x = 180 + 54

-9x = 234 - 360

x = 14

Therefore, the value of x is 14.

---

Find the value of x. The diagram is not to scale. Given RS = ST, m RST = 7x - 54, mSTU = 8x

Summary:

Given RS = ST, m RST = 7x - 54, mSTU = 8x, the value of x is 14.