Name: More About the Angles: Adjacent Angles
Uploaded: 2019-07-19
Duration: 6 min 42 s
Description: Adjacent angles are two angles that have a common vertex and a common side but do not overlap. We will learn more about them and how to draw them in this video.

Question

Of the four angles made by two lines crossing each other, one angle is half of another angle. Calculate all four angles.

Accepted Answer

Consider the figure in which two lines $A B$ and $C D$ crossing each other at a point $O$ forming four angles,

Namely, $∠ A O D, ∠ B O D, ∠ B O C$ and $∠ A O C$ .

According to the question, let $∠ B O D = 2 x °$ and $∠ A O D = x °$ .

Also, $∠ A O D$ and $∠ B O D$ form a linear pair.

We know that the sum of the angles in a linear pair is $180 °$ .

$\Rightarrow$ $∠ A O D + ∠ B O D = 180 °$

$\Rightarrow x ° + 2 x ° = 180 °$

$\Rightarrow 3 x ° = 180 °$

$\Rightarrow x ° = \frac{180 °}{3} = 60 °$

Now, $∠ B O D = 2 x ° = 2 \times 60 ° = 120 °$ .

When two lines cross each other, each pair of vertically opposite angles formed are equal.

$∠ A O C = ∠ B O D = 120 °$ and $∠ B O C = ∠ A O D = 60 °$ .

Hence, the required angles are $60 °, 120 °, 60 °$ and $120 °$ .

Of the four angles made by two lines crossing each other, one angle is half of another angle. Calculate all four angles.

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