In ΔABC ∠ACB = 120º and ∠CAB = 40º. AC is extende

Question

In ΔABC ∠ACB = 120º and ∠CAB = 40º. AC is extended to P such that AP = AC + 2CB. The measure of ∠ABP is 1) 60º2) 120º3) 110º4) 100º

Arun · Accepted Answer

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........(1)GivenAP=AC+2CBor AC+CP=AC+2CBCP=2CB........(2)CM+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 pair]So finally triangle BMCis equilateral triangle.So CM=MBNow using equation 1, MP=MBSo in triangle BMP, ∠MBP=∠MPB.............(3)Using angle sum property in triangle MPB, ∠MBP+∠MPB+120=180or ∠MBP+∠MBP=60∠MBP=30 degreeSo angle ABP=20+60+30=110 degree

7 grade maths> In ΔABC ∠ACB = 120º and ∠CAB = 40º. AC is...

In ΔABC ∠ACB = 120º and ∠CAB = 40º. AC is extended to P such that AP = AC + 2CB. The measure of ∠ABP is

1) 60º
2) 120º
3) 110º
4) 100º

Rahul Sanapala , 6 Years ago

Arun

Rahul Sanapala

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7 grade maths> In ΔABC ∠ACB = 120º and ∠CAB = 40º. AC is...

In ΔABC ∠ACB = 120º and ∠CAB = 40º. AC is extended to P such that AP = AC + 2CB. The measure of ∠ABP is 1) 60º2) 120º3) 110º4) 100º

Rahul Sanapala , 6 Years ago

Arun

Rahul Sanapala

LIVE ONLINE CLASSES

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7 grade maths

In ΔABC ∠ACB = 120º and ∠CAB = 40º. AC is extended to P such that AP = AC + 2CB. The measure of ∠ABP is

1) 60º
2) 120º
3) 110º
4) 100º

Find the following percentage value:
1) 15% of 250.

Convert 1 gallon into liters.
a. 3.05 liters
b. 3.78 liters
c. 4.05 liters
d. 4.78 liters