Question

in the figure, AOB is a straight line. Express y in terms of x.

Answer 1

SINCE AOB IS A STRAIGHT LINE, AND GIVEN <AOC = < COD = x

<AOB = 180°
THEREFORE, <AOC + <COD + <DOB = 180°
x + x + y = 180°
2x + y = 180°
y = 180° - 2x

HENCE PROVED.

Answer 2

Question :-

In figure, if x + y = w + z, then prove that AOB is a line.

Answer :-

Sum of all the angles at a point = 360°

∴ x + y + z + w = 360° or, (x + y) + (z + w) = 360°

But (x + y) = (z + w) [Given]

∴ (x + y) + (x + y) = 360° or,

2(x + y) = 360°

or, (x + y) = 360° /2 = 180°

∴ AOB is a straight line.

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