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 + 6)° and m∠rst = (8x − 26)°, 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 =

We make use of the Definition of Angle Bisector. Suppose you draw an angle labeled RST where the vertex is at point S, as shown in the attached picture. The angle bisector is a line segment that is drawn from the vertex S and extended outwards, such that it divides the angle into two equal parts. In this case, the angle bisector is line segment SV. The orange angle represents the total angle equal to (8x-14)°. The half of the angle, denoted as the red curve, represents (3x + 5)°. The equation to be used is:

∠RST = 2×∠RSV

This comes from the Angle Addition Postulate. This postulate states that all the interior angles within the total angle are additive. Since ∠RSV = ∠VRT, then ∠RSV + ∠VRT is just equivalent to 2×∠RSV. Continuing the solution,

8x - 14 = 2(3x+5)
8x-14 = 6x + 10
8x - 6x = 10+14
2x = 24
x = 24/2
x = 12°

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