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

Accepted Solution

Answer:Part 1) x=5Part 2) m∠DEG=112°Part 3) m∠GEF=68°Part 4) m∠DEF=180°Step-by-step explanation:step 1 Find the value of xwe know thatIf m∠DEF is a straight anglethen m∠DEF=180°m∠DEF=m∠DEG+m∠GEFso180°=m∠DEG+m∠GEFsubstitute the given values180°=(23x-3)°+(12x+8)°solve for x180=35x+535x=180-535x=175x=5step 2Find the measure of angle DEGm∠DEG=(23x-3)°substitute the value of xm∠DEG=(23(5)-3)°m∠DEG=112°step 3Find the measure of angle GEFm∠GEF=(12x+8)°substitute the value of xm∠GEF=(12(5)+8)°m∠GEF=68°step 4 Find the measure of angle DEFm∠DEF=m∠DEG+m∠GEFwe havem∠DEG=112°m∠GEF=68°substitutem∠DEF=112°+68°m∠DEF=180° ----> is correct (the straight angle measure 180 degrees)