Answer:
x = 9
Step-by-step explanation:
Exterior Angle property of a triangle:
The Exterior Angle property states that:
"The exterior angle of a triangle(the Angle obtained by extending one of the sides of the triangle) is equal to the sum of it's interior opposite angles."
In the given triangle RST:
∠VRS is the exterior angle, and
∠RTS and ∠RST are the interior opposite angles.
By using the above listed property,
∠VRS = ∠RTS + ∠RST
(Substituting the values of of angles from the figure)
=> (9x + 2) = 51 + (3x + 5)
=> 9x + 2 = 51 + 3x + 5
isolating x
=> 9x - 3x = 51 + 5 - 2
=> 6x = 54
dividing both sides by 6
=> x = 9
