Name: Parallel & Transversal Lines: Illustration
Uploaded: 2019-07-19
Duration: 6 min 20 s
Description: In geometry, the straight lines which do not meet are called parallel. A line that crosses a pair of parallel lines is known as transversal. Watch and learn...

Question

In the below given figure $A B$ and $C D$ are two straight lines intersecting each other at $O$ .If $∠ C O E = 90 °$ , find the values of $x, y$ and $z$ .

Accepted Answer

Given, $A B$ and $C D$ are two lines intersecting at point $O$ , and $∠ C O E = 90 °$

We know the sum of angles at a point on a line $= 180 °$

So, $∠ A O C + ∠ C O E + ∠ B O E = 180 °$

$\Rightarrow 2 x + 90 ° + x = 180 °$

$\Rightarrow 3 x = 180 ° - 90 °$

$\Rightarrow 3 x = 90 °$

$\Rightarrow x = \frac{90 °}{3} = 30 °$

$\Rightarrow x = 30 °$

Similarly,

$∠ C O E + ∠ B O E + ∠ B O D = 180 °$ [ Linear pair ]

$\Rightarrow 90 ° + 30 + y = 180 °$

$\Rightarrow y = 180 ° - 120 °$

$\Rightarrow y = 60 °$

$∵ ∠ A O D = ∠ B O C$ [ Vertically opposite angles ]

$\Rightarrow z = 90 + x$

$z = 90 + 30 = 120 °$

Hence, the values of $x, y$ and $z$ are $30 °, 60 °$ and $120 °$ respectively.

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