Question

If DEF is a straight angle, mDEG = (23r-3)and mGEF = 112x+8).
find each measure.​

Answer 1

Part 1) x=5

Part 2) m∠DEG=112°

Part 3) m∠GEF=68°

Part 4) m∠DEF=180°

Explanation:

step 1

Find the value of x

we know that

If m∠DEF is a straight angle

then

m∠DEF=180°

m∠DEF=m∠DEG+m∠GEF

so

180°=m∠DEG+m∠GEF

substitute the given values

180°=(23x-3)°+(12x+8)°

solve for x

180=35x+5

35x=180-5

35x=175

x=5

step 2

Find the measure of angle DEG

m∠DEG=(23x-3)°

substitute the value of x

m∠DEG=(23(5)-3)°

m∠DEG=112°

step 3

Find the measure of angle GEF

m∠GEF=(12x+8)°

substitute the value of x

m∠GEF=(12(5)+8)°

m∠GEF=68°

step 4

Find the measure of angle DEF

m∠DEF=m∠DEG+m∠GEF

we have

m∠DEG=112°

m∠GEF=68°

substitute

m∠DEF=112°+68°

m∠DEF=180° ----> is correct (the straight angle measure 180 degrees)