Question

In the following figure, if ∠ 1 + ∠ 2 = 100°, then the measure of ∠ 4 is equal to ..... .
Plz give ANS with method​

Answer 1

Answer:

130°

The calculations is as follows:

∠ 1 + ∠ 2 = 100°

And because they are Vertically Opposite Angles,

∠ 1 = ∠ 2

So, ∠ 1 + ∠ 2 =100

2∠ 1 =100

∠ 1 = 50°

and ∠ 2 = 50°

Now,

∠ 4+ ∠ 2 = 180° (As they are linear pairs)

∠ 4+ 50° = 180°

∠ 4 = 180°-50

∠ 4 = 130°

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Answer 2

Given :  ∠ 1 + ∠ 2 = 100°

To Find : the measure of ∠ 4

Solution:

Method 1:

Vertically opposite angles are equal

Hence ∠ 1= ∠ 2

∠ 1 + ∠ 2 = 100°

=> 2∠ 1  = 100°

=> ∠ 1  = 50°

∠ 1  and ∠ 4  form linear pair

Hence ∠ 1 + ∠ 4 = 180°

=>  50°  + ∠ 4 = 180°

=> ∠ 4 = 130°

Method  2 :

∠ 1 + ∠ 4 = 180°  linear pair

∠ 2 + ∠ 4 = 180°  linear pair

Adding both

∠ 1 + ∠ 2  + 2∠ 4 = 360°

=>  100° + 2∠ 4 = 360°

=> 2∠ 4 = 260°

=> ∠ 4 = 260°/2

=> ∠ 4 = 130°

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