Question

Use a definition, postulate, or theorem to find the value of x in the figure described. SV is an angle bisector of ∠RST. If m∠RSV = (3x + 9)° and m∠RST = (8x − 20)°, find x. Select each definition, postulate, or theorem you will use. A Linear Pair Theorem B definition of angle bisector C Angle Addition Postulate D definition of midpoint The solution is x =

Answer 1

It is given in the question that SV is an angle bisector of ∠RST.

And

$m\angle RSV = 3x + 9 \ and \ m\angle RST = 8x-20$

And since SV is the angle bisector, therefore

$m \angle RSV = \frac{1}{2} m \angle RST$

$3x+9 = \frac{1}{2}(8x-20)$

On cross multiplication, we will get

$6x+18 = 8x-20 \\ 18+20 = 8x-6x \\ 2x = 38 \\ x=19$

And the correct option is B