Name: Introduction to Triangles and its Properties
Uploaded: 2019-07-19
Duration: 33 min 54 s
Description: In this video, basic concepts of Triangles, different types of Triangles and its properties are discussed. The content in this video is helpful to solve the related problems on this topic.

Question

The line $A B$ and $P Q$ are parallel and the line $X Y$ cuts them at $C$ and $R$ . Find all the pairs of co-interior angles and co-exterior angles and write their names and measures.

Accepted Answer

Given figure,

As we can see, the line $P Q$ and $P Q$ are parallel and the line $C$ cuts them at $C$ and $R$ .

We have to find all the pairs of co-interior angles and co-exterior angles with their names and measures.

Co-interior angles lie between two lines and on the same side of a transversal. In the given diagram the two angles within the side of $60 °$ are called co-interior angles. If the two lines are parallel, then co-interior angles add to give 180^o and so are supplementary.

From the figure we can write that the angles formed by the transverse upon the two parallel lines in the interior area which means within the two parallel line as co- interior angles whereas angle outside the parallel line on the same side as co- exterior angle.

Co-interior angles Co- exterior angle

$∠ A C R, ∠ P R C$ $∠ A C X, ∠ P R Y$

$∠ B C R, ∠ Q R C$ $∠ B C X, ∠ Q R Y$

As it is given that the value of $∠ A C R = 60 °$ and the sum of the co-interior angles is $180 °$ .

Hence, we can write,

$\Rightarrow ∠ A C R + ∠ P R C = 180 °$

$\Rightarrow 60 ° + ∠ P R C = 180 °$

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

Now for $∠ B C R, ∠ Q R C$ we can use alternate angles rule, which states that alternate angles formed by a transverse over two parallel lines are always equal.

Hence, we can write,

$\Rightarrow ∠ B C R = ∠ P R C = 120 °$

$\Rightarrow ∠ Q R C = ∠ A C R = 60 °$

Now we have to find the co- exterior angle for that we need any one co- exterior angle first and then we will proceed.

Since we can see $X Y$ is a straight line with sum of $∠ A C X, ∠ A C R$ equal to $180 °$ .

$\Rightarrow ∠ A C X + ∠ A C R = 180 °$

$\Rightarrow ∠ A C X + 60 ° = 180 °$

$\Rightarrow ∠ A C X = 180 ° - 60 ° = 120 °$

Now as we know the sum of the co-exterior angles is $180 °$ so we can write,

$\Rightarrow ∠ A C X + ∠ P R Y = 180 °$

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

Now for $∠ B C X, ∠ Q R Y$ we can use alternate angles rule, which states that alternate angles formed by a transverse over two parallel lines are always equal.

Hence, we can write,

$\Rightarrow ∠ B C X = ∠ P R Y = 60 °$

$\Rightarrow ∠ Q R Y = ∠ A C X = 120 °$

So finally we can write:

Co-interior angles Co- exterior angle

$∠ A C R = 60 °, ∠ P R C = 120 °$ $∠ A C X = 120 °, ∠ P R Y = 60 °$

$∠ B C R = 120 °, ∠ Q R C = 60 °$ $∠ B C X = 60 °, ∠ Q R Y = 120 °$

The line $A B$ and $P Q$ are parallel and the line $X Y$ cuts them at $C$ and $R$ . Find all the pairs of co-interior angles and co-exterior angles and write their names and measures.

Important Questions on Parallel Lines

Learn and Prepare for any exam you want !

The line AB and PQ are parallel and the line XY cuts them at C and R. Find all the pairs of co-interior angles and co-exterior angles and write their names and measures.

Important Questions on Parallel Lines

Learn and Prepare for any exam you want !

The line $A B$ and $P Q$ are parallel and the line $X Y$ cuts them at $C$ and $R$ . Find all the pairs of co-interior angles and co-exterior angles and write their names and measures.