Question

Line SV is an angle bisector of angle RST if angle RSV = (3x+5) and angle RST = (8x-14) find x

Answer 1

SV splits RST into 2 equal sections.

so RST = 2 * RSV

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

Answer 2

x=12

Explanation:

Line SV is an angle bisector of angle RST

<RSV = <VST

Both angles are equal

m<RSV = (3x+5)

<RSV = <VST, so m<VST = (3x+5), m<RST= 8x-14

m<RST= m<RSV +m<VST

`8x-14= 3x+5+3x+5`

Combine like terms and solve for x

`8x-14= 6x+10`

Subtract 6x from both sides

`2x-14=10`

Add 14 on both sides

`2x=24`

Divide both sides by 2

x=12