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

Two pictures of lines passing through a point are given. Some angles are given. Calculate the other angles marked.

Accepted Answer

Consider the given figure as shown.

In the figure, $∠ A O C = 90 °$ and $∠ B O F = 40 °$ .

Here, we observe that $∠ A O C$ and $∠ B O C$ form a linear pair.

$∴ ∠ A O C + ∠ B O C = 180 °$

$\Rightarrow ∠ A O C + ∠ C O F + ∠ B O F = 180 °$

$\Rightarrow 90 ° + ∠ C O F + 40 ° = 180 °$

$\Rightarrow 130 ° + ∠ C O F = 180 °$

$\Rightarrow ∠ C O F = 180 ° - 130 ° = 50 °$

We know that vertically opposite angles are equal.

Now, let us write each pair of vertically opposite angles with their measures.

$∠ C O F = ∠ E O D = 50 °$ , $∠ B O D = ∠ A O C = 90 °$ ,

$∠ A O E = ∠ B O F = 40 °$

Consider another given figure as shown.

We know that vertically opposite angles are equal.

$∴ ∠ I X L = ∠ K X J = 60 °$ and $∠ J X H = ∠ G X I = 50 °$ .

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

From the figure, $∠ G X K$ and $∠ K X H$ form a linear pair.

So, $∠ G X K + ∠ K X H = 180 °$

$\Rightarrow ∠ G X K + ∠ K X J + ∠ J X H = 180 °$

$\Rightarrow ∠ G X K + 60 ° + 50 ° = 180 °$

$\Rightarrow ∠ G X K + 110 ° = 180 °$

$\Rightarrow ∠ G X K = 180 ° - 110 ° = 70 °$

Now, $∠ L X H$ and $∠ G X K$ are the pair of vertically opposite angles.

$∴ ∠ L X H = ∠ G X K = 70 °$ .

Kerala Board Solutions for Chapter: Joining Angles, Exercise 7: Exercise 7

Kerala Board Mathematics Solutions for Exercise - Kerala Board Solutions for Chapter: Joining Angles, Exercise 7: Exercise 7

Questions from Kerala Board Solutions for Chapter: Joining Angles, Exercise 7: Exercise 7 with Hints & Solutions

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