Question

If mZGEF is thirteen less than five times

mZDEG and mZDEF = 149°, find mZGEF.
F
D
G

Answer 1

Explanation:

Given :

From the diagram,

m∠GEF is 13 less than 5 times m∠DEG and ∠DEF = 149°,.

To Find :

the value of m∠GEF..

Solution :

As per given data,

m∠GEF = 5m∠DEG - 13° ...(i)

∠DEF = 149° ⇒ m∠GEF + m∠DEG = 149° ..(ii)

Substituting value of m∠GEF in (ii),

We get,

(5m∠DEG - 13°) + m∠DEG = 149°

6m∠DEG - 13° = 149°

6m∠DEG = 149° + 13° = 162°

m∠DEG = ° = 27°

Substituting value of m∠DEG in (i),

We get,

m∠GEF = 5(27°) - 13°

m∠GEF = 135° - 13°= 122°