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In the figure given below, if $∠ A O C$ and $∠ B O C$ and form a linear pair such that $a − 2 b = 30 °,$ form a linear pair such that then what are the measures of angles $a$ then what are the measures of angles and $b$ and ? ?

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130 °

and

50 °

30 °

and

30 °

140 °

and

50 °

30 °

and

40 °

answer is A.

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Detailed Solution

It is given that

∠ A O C

and

∠ B O C

form a linear pair such that

a − 2 b = 30 ° .

Using the linear pair property, we have,

∠ A O C + ∠ B O C = 180 °

a + b = 180 ° (1)

Given,

a − 2 b = 30 ° (2)

Subtracting equation (2) from (1), we get,

3 b = 150 ° ⇒ b = 50 °

∵ a + b = 180 ° ⇒ a + 50 ° = 180 ° ⇒ a = 130 °

Therefore, the measures of angles

a

and

b

are respectively

130 °

and

50 ° .

Hence, option (1) is correct.

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