If the measure of angle GEF is thirteen less than 5 times the measure of angle DEG and the measure of angle DEF is 149°, find the measure of angle GEF.
Accepted Solution
A:
Answer:122°Step-by-step explanation:Answer:
Step-by-step 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°