Question

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.

Answer 1

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°

Answer 2

• The measure of m<GEF give that m<DEF is 149degrees is 122 degrees
• Angles are points where two or more lines meet.

From the diagram shown:

m<DEG + m<GEF = m<DEF ........1

Given the following:

m<DEF = 149 degrees

If m<GEF is thirteen less than 5 times the measure of angle DEG, then:

• m<GEF = 5m<DEG - 13 .... 2

Substitute equation 2 into 1

m<DEG + 5m<DEG - 13 = 149

6m<DEG = 149 + 13

6m<DEG = 162

m<DEG = 162/6

m<DEG = 27

Get the angle GEF

Recall that

• m<GEF = 5m<DEG - 13

m<GEF = 5(27) - 13

m<GEF = 135 - 13

m<GEF = 122 degrees

Hence the measure of m<GEF is 122 degrees

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