Question

What is the value of X

Answer 1

an outside angle is equal to the two opposite angles inside the triangle
9x=5x+9+x
9x=6x+9
-6x both sides
3x=9
÷3 both sides
x=3

Answer 2

The value of x = 3

Explanation:

In ΔRTS

Exterior Angle theorem: An Exterior angle of a triangle is equal to the sum of the opposite interior angles.

In the given triangle RST,

`\angle TRQ = (9x)^(\circ)` is the exterior angle of the triangle RTS

and
`\angle RTS= (5x)^(\circ)` and
`\angle TSR = (9+x)^(\circ)` are the two opposite interior angles.

Therefore, by the definition of Exterior Angle theorem;

`\angle TRQ = \angle RTS + \angle TSR`

Then;

`9x=5x+9+x`

Combine like terms,

9x = 6x+9

Subtract 6x from both the sides we get;

9x - 6x = 6x+9-6x

Simplify:

3x = 9

Divide by 3 we get;

`(3x)/(3) = (9)/(3)`

Simplify:

x= 3