In the diagram above, TRQ is a straight line. Find p, if p = \(\frac{1}{3}\)(a + b + c)

Dammy198627

2 years ago

1/3(a+b+c)+(a+b+c) = 180 (sum of angles on a str. line)
a+b+c+3a+3b+3c=540
4a+4b+4c=540
4(a+b+c)=540
a+b+c=135
But, p =1/3(a+b+c) = 1/3 (135) = 45

damilaresemako

1 year ago

i Need the explanation

melzito

2 years ago

a+b+c+p=180 (angles on straight line)
a+b+c=180-p (subtract p from both sides)
(a+b+c)/3=(180-p)/3 (divine both sides by 3)
p=(180-p)/3 (since question says a+b+c/3 =p therfore convert)
3p=180-p (multiply both sides by 3)
4p=180 (add p to both sides)
p=45 (divide both sides by 4)