Consider the following figure:

A and B are points on the line $\leftarrow \to A B, \leftarrow \to O C, \leftarrow \to O D a n d \leftarrow \to O E$ are rays with point O on the line $\leftarrow \to A B$ . The angles AOC, COD, DOB, AOE, EOB are given by a, b, c, x and y respectively.

Choose the incorrect statement:

a + b + c = x + y

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x and y form a linear pair of angles

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a + b + c + x + y = 360°

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x and y are complementary

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Solution

The correct option is D
x and y are complementary

As AB is a straight line, a+b+c = $180^{\circ}$ .
Also, x and y form a linear pair, so that x+y = $180^{\circ}$ = a+b+c
Thus, a+b+c+x+y = $360^{\circ}$
As sum of angles that form complementary angles is $90^{\circ}$ , therefore, x and y are not complementary angles.

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Consider the following figure: A and B are points on the line ←→AB,←→OC,←→OD and ←→OE are rays with point O on the line ←→AB . The angles AOC, COD, DOB, AOE, EOB are given by a, b, c, x and y respectively. Choose the incorrect statement:

The correct option is D x and y are complementary As AB is a straight line, a+b+c = 180∘. Also, x and y form a linear pair, so that x+y = 180∘ = a+b+c Thus, a+b+c+x+y = 360∘ As sum of angles that form complementary angles is 90∘, therefore, x and y are not complementary angles.