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What is the value of X

What is the value of X-example-1

2 Answers

1 vote
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
User Guy Bolton King
by
6.2k points
5 votes

Answer:

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




User Liam Potter
by
6.6k points