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 = (2x + 8)° and m∠RST = (6x − 24)°, find x.

Select each definition, postulate, or theorem you will use.

A Linear Pair Theorem
B definition of midpoint
C Angle Addition Postulate
D definition of angle bisector

The solution is x =
.

Answer 1

we know that

An angle bisector is a line or ray that divides an angle into two congruent angles

so

in this problem

m∠RST=m∠RSV+m∠VST

m∠RSV=m∠VST

hence

m∠RST=2*m∠RSV --------> equation 1

we have

m∠RST=(6x-24)

m∠RSV=(2x+8)

Substitute in the equation 1

6x-24=2*(2x+8)

6x-24=4x+16

6x-4x=16+24

2x=40

x=40/2

x=20 degrees

therefore

the answer is the option

D definition of angle bisector

and the value of x is 20 degrees