Challenge In triangleABC,mangleBtriangleABC,mangleB is one-thirdthe mangleAmangleA and mangleCmangleC is 37 less than themangleA.mangleA. What are the measures of theangles of triangleABC?

Bevan Mcdonald

Bevan Mcdonald

Answered question

2021-01-13

Challenge In ABC,mB is one-third the mA and mC is 37 less than the mA.. What are the measures of the angles of ABC?

Answer & Explanation

Clara Reese

Clara Reese

Skilled2021-01-14Added 120 answers

in triangle ABC

mB=(13)mA --------- ( 1 )

mC=mA37 ------------ ( 2 )

the sum of the internal angles of a triangle = 180 thus

mA+mB+mC=180 ----------- ( 3 )

compensate from ( 1 ) and ( 2 ) in ( 3 ) mA+(13)mA+(mA37)=180(73)mA37=180 ( add 37 to both sides ) (73)mA=180+37=217 ( multiply both sides by (37)mA=217(37)=31×3=93mA=93

compensate in ( 1) by mA=93m<B=(1/3)×93=(93/3)=31 compensate in ( 2 ) by m<A=93mC=9337=56 thus mA=93mB=31m<C=56

answer measures of the angles of the triangle ABC : mA=93mB=31mC=56

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