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Examples of Lines and angles

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(1) AB and CD are two parallel lines. Find x, y and z.

Soln. x = 70⁰ ( Vertically opposite angles. )

Now, y = x = 70⁰ ( Alternate angles (Z). )

And, z = 180⁰ – y ( $\because$ y and z are supplementary angles. )

= 110⁰

(2) From the given figure, calculate a and b.

Soln. Here, b₁ = 40⁰ ( Alternate angles (Z). )

And b₂ = 25⁰ ( Alternate angles (Z). )

b = b₁ + b₂ = 65⁰

And a = 360⁰ – 65⁰ = 295⁰ ( a + b = Complete angles. )

(3) Calculate x.

Soln. The sum of all angles = 180^o $\large \Rightarrow$ 8x + 2x + 5x = 180

15x = 180⁰ x = 12⁰.

(4) Find x.

Soln. The sum of all angles is 360⁰

$\large \Rightarrow$ 3x + 30⁰ + 69⁰ = 360⁰

$\large \Rightarrow$ 3x = 360⁰ – 99⁰ = 261⁰ $\large \Rightarrow$ x = 87⁰.

(5) Find x.

Soln. 145⁰ + 90⁰ + 82⁰ + x = 360⁰ $\therefore$ x = 360⁰ – 317⁰ = 43⁰