Question

The sidevBA and DC of a quadrilateral are produced as shown in the given figure.

Prove that x+y = a+b​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

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Question

•The side BA and DC of a quadrilateral are produced as shown in figure.

Prove that x+y = a+b

To prove

• x+y = a+b

Proof

We have ∠A + b° = 180° (linear pair)

==> ∠A = (180°– b°) ... (i)

Also, ∠C + a° = 180° (linear pair)

==> ∠C = (180°– a°) ... (ii)

Now, ∠A + ∠B + ∠C + ∠D = 360° (sum of all angles of quadrilateral is 360°)

==> (180°– b°) + x + (180°– a°) + y = 360° [using (i) and (ii) equation)

==> 360 – a –b + x + y = 360

==> – a – b +x + y = 0° (as 360° is being cancelled out by the 360° on another side)

==> x + y = a+b

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☙Sum of two angles created on a straight line is 180° by linear pair.

☙Sum of all angles of quadrilateral is 360°

━─━─━─━─━──━─━─━─━─━─━─━━─━─━─━─━──━─━─━─━─━─━─━━─━─━

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•In quadrilateral we have:-

☙Vertices :-The point are called the vertices of quadrilateral.

☙Sides:-The line segment are called the sides of quadrilateral.

☙Adjacent Sides:-Two sides of a quadrilateral having a common endpoint are called it consecutive or adjacent side.

☙Opposite Sides:-Two sides of a quadrilateral having no endpoint are called its opposite side.

☙Consecutive Angles:-Two angles of a quadrilateral having a common are called its consecutive angle.

☙Opposite Angles:-Two angles of a quadrilateral having no common are called its opposite angle.