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if a ray stands on a line and a angle is greater than b angle by one third of a right angle,find the value of a and b
We know that if a straight line stands upon another,
the sum of the adjacent angles so formed is equal to 180 degrees
Here the adjacent angles are given to be A and B
Therefore (A+B)= 180 ----(1)
And now by data A is greater than B by (1/3)of a right angle.
One right angle =90 degrees
(1/3) of a right angle = (1/3)X(90) = 30 degrees
Therefore A>B by 30 degrees.
That is A = B+30 ----(2)
Putting (2) in (1),that is substituting for A in (1), we have
(B+30) + B = 180
2B = 150
B=150/2 = 75 degrees
B=75 in (1) gives
A+75 = 180
A=180-75 = 105
Answer: Angle A = 105 degrees and angle B = 75 degrees
Verification: A should be greater than B by 30 degrees.
Of course 105 is 30 more than 75
Therefore our angles are correct.