Answer:
The value of x = 3
Step-by-step 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,
[tex]\angle TRQ = (9x)^{\circ}[/tex] is the exterior angle of the triangle RTS
and [tex]\angle RTS= (5x)^{\circ}[/tex] and [tex]\angle TSR = (9+x)^{\circ}[/tex] are the two opposite interior angles.
Therefore, by the definition of Exterior Angle theorem;
[tex]\angle TRQ = \angle RTS + \angle TSR[/tex]
Then;
[tex]9x=5x+9+x[/tex]
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;
[tex]\frac{3x}{3} = \frac{9}{3}[/tex]
Simplify:
x= 3
