Question

Solve for x
solve for x
please :)

Answer 1

x = 3

Explanation:

Pre-Solving

We are given triangle RTS. We can see that the points R and S are on the line QS.

We know that m<T = 25x, m<S = 57 + x and m<TRQ = 45x

We want to find the value of x.

Recall the exterior angle theorem: the measure of an exterior angle is equal to the sum of the two remote interior angles.

We can see that <TQR is an exterior angle - that is, it is outside of triangle RTS.

Solving

This means m<T + m<S = m<TQR

So:

25x + 57 + x = 45x

26x + 57 = 45x

Subtract 26x from both sides.

57 = 19x

Divide both sides by 19.

3 = x

Answer 2

Explanation:

`(25x) + (57 + x) = (45x) (ext. \: angles \: of \: a \: triangle) \\ 25x + x- 45x = - 57 \\ ( - 19x)/( - 19) = ( - 57)/( - 19) \\ x = 3`

Goodluck