in triangle ABC,angle ACB is equals to 120 and CAB is equals to 40 AC is extented to P - Maths - Triangles

Question

in triangle ABC,angle ACB is equals to 120 and CAB is equals to
40 AC is extented to P such that AP=AC+2CB,then angle ABP= ?

Anuradha Sharma · Accepted Answer

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Here angle ACB=120 and angle CAB=40 degreeSo Angle ABC= 180-120-40-20 degreeand using linear pair property, ∠BCP=180-120=60 degreeNow lets take mid point of CP as M and then CM=MP
1GivenAP=AC+2CBor AC+CP=AC+2CBCP=2CB
2CM+MP=2CBCM+CM=2CB2CM=2CBCM=CBmeans triangle CMB is isosceles, So in triangle BMC, ∠CMB=∠CBMUsing angle sum property in  triangle BMC∠CMB+∠CBM=180-60=120or ∠CMB=∠CBM=60 degreeSo angle BMP= 180-60=120 degree Linear pairSo finally triangle BMC is equilateral triangle
So CM=MBNow using equation 1, MP=MBSo in triangle BMP, ∠MBP=∠MPB
3Using angle sum property in triangle MPB, ∠MBP+∠MPB+120=180or ∠MBP+∠MBP=60∠MBP=30 degreeSo angle ABP=20+60+30=110 degree

in triangle ABC,angle ACB is equals to 120 and CAB is equals to 40 .AC is extented to P such that AP=AC+2CB,then angle ABP= ?