Question

If the measure of angle GEF is thirteen less than five times measure of angle DEG and measure of of DEF = 149 degrees, find measure of angle GEF

Answer 1

def=149

gef=5x-13

deg=x

5x-13+x=149

6x=162

x=27

plug the x back in

5(27)-13=122

Answer 2

122 degrees

Explanation:

Find the diagram attached. From the diagram;

<DEG + <GEF = <DEF

If the measure of angle GEF is thirteen less than five times measure of angle DEG, this is expressed as;

<GEF = 5<DEG - 13

Substitute

<DEG + <GEF = <DEF

<DEG + 5DEG - 13 = <DEF

6<DEG - 13 = <DEF

6<DEG - 13 = 149

6<DEG = 149 + 13

6<DEG = 162

<DEG = 27

Since <GEF = 5<DEG - 13

<GEF = 5(27) - 13

<GEF = 135-13

<GEF = 122 degrees

Hence the measure of angle GEF is 122degrees