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

Some pictures showing two lines crossing each other are given. One of the angle so formed is given. Calculate the other three angles.

Accepted Answer

Consider the figure as shown, in which the line segments $A B$ and $C D$ intersect each other at $O$ .

Here, we observe that four different angles are formed.

$∠ A O C$ and $∠ B O C$ form a linear pair.

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

$∴ ∠ A O C + ∠ B O C = 180 °$

$\Rightarrow ∠ A O C + 45 ° = 180 °$

$\Rightarrow ∠ A O C = 180 ° - 45 ° = 135 °$

Now, $∠ B O C$ and $∠ A O D$ are the pair of vertically opposite angles.

We know that vertically opposite angles are equal.

$∴ ∠ A O D = ∠ B O C = 45 °$ .

Similarly. $∠ A O C$ and $∠ B O D$ are the pair of vertically opposite angles.

Then, $∠ B O D = ∠ A O C = 135 °$

Consider second picture as shown in the figure, in which $P Q$ and $R S$ intersect at $X$ .

Here, we observe that four different angles are formed.

$∠ P X S$ and $∠ P X R$ form a linear pair.

$∴ ∠ P X S + ∠ P X R = 180 °$

$\Rightarrow 120 ° + ∠ P X R = 180 °$

$\Rightarrow ∠ P X R = 180 ° - 120 ° = 60 °$

Now, $∠ P X S$ and $∠ R X Q$ are the pair of vertically opposite angles.

We know that vertically opposite angles are equal.

$∴ ∠ P X S = ∠ R X Q = 120 °$

Similarly, $∠ P X R$ and $∠ S X Q$ are the pair of vertically opposite angles.

$∴ ∠ P X R = ∠ S X Q = 60 °$

Consider another given picture as shown in the figure.

Here, line segments $E F$ and $G H$ intersects at a point $Y$ .

$∠ H Y E$ and $∠ H Y F$ form a linear pair.

$∴ ∠ H Y E + ∠ H Y F = 180 °$

$\Rightarrow ∠ H Y E + 90 ° = 180 °$

$\Rightarrow ∠ H Y E = 180 ° - 90 ° = 90 °$

Now, $∠ H Y F$ and $∠ E Y G$ are the pair of vertically opposite angles.

$∴ ∠ H Y F = ∠ E Y G = 90 °$

Similarly, $∠ H Y E$ and $∠ G Y E$ are the pair of vertically opposite angles.

$\Rightarrow ∠ H Y E = ∠ G Y E = 90 °$

Some pictures showing two lines crossing each other are given. One of the angle so formed is given. Calculate the other three angles.

Important Questions on Joining Angles

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