Question

What is the value of x?

Answer 1

x = 3

Explanation:

The external angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠TRQ is an external angle and ∠RTS, ∠RST are interior angles, hence

45x = 25x + 57 + x

45x = 26x + 57 ( subtract 26x from both sides )

19x = 57 ( divide both sides by 19 )

x = 3

Answer 2

x = 3

Explanation:

We are given expression for measure of angles of two corners of a triangle, while for the third corner, we know the exterior angle.

We know that the sum of all three angles of a triangle is 180°.

So we can write it as:

`2 5 x + ( 5 7 + x ) + ( 1 8 0 - 4 5 x ) = 180`

`25x+x-45x=180-180-57`

`-19x=-57`

`x=(-57)/(-19)`

x = 3