Question

LINES AND ANGLES
10.15
5. In Fig. 10.35, ZAOC and ZBOC form a linear pair. If a – 2b = 30°, find a and b.
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Answer 1

a+b=180 (linear pair)

a=180-b

a-2b =30

180-b-2b=30

180-3b=30

180-30=3b

150=3b

50=b

b=50

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Answer

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Given

angle AOC and angle BOC form a linear pair.

angle AOC =a , angle BOC=b

and a-2b=30.

Find the  value of a and b .

To proof

As given

angle AOC and angle BOC form a linear pair

∠AOC + ∠BOC = 180°

put the value

a + b = 180

than the two equation becomes

a-2b=30 and a + b = 180

multiply  a + b = 180 by 2 and subtracted from a-2b=30

2a + 2b - 2a + 4b = 360 - 60

6b = 300

b = 50

put this in the equation a + b = 180

a + 50 =180

a = 130

the value of a = 130 and b = 50

Hence proved