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 figure, $l ∥ m$ . Find the values of $x, y, z, w$

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Accepted Answer

Given,

In the figure, $l ∥ m$ ,

If a transversal intersects a pair of parallel lines, Alternate interior angles are equal.

Thus, $∠ x = 35^{°}$

Corresponding angles are equal.

Thus, $∠ z = 70^{°}$

The sum of angles of a linear pair is always equal to $180^{°}$ . Such angles are also known as supplementary angles.

Thus, $∠ w + 35^{°} = 180^{°}$

$∠ w = 180^{°} - 35^{°}$

$∠ w = 145^{°}$

The sum of all the angles at a point of a straight line on one side of the straight line is $180^{°}$ .

Thus, $∠ z + ∠ y + ∠ x = 180^{°}$

$70^{°} + ∠ y + 35^{°} = 180^{°}$

$105^{°} + ∠ y = 180^{°}$

$∠ y = 180^{°} - 105^{°}$

$∠ y = 75^{°}$

Hence, $∠ x = 35^{°}, ∠ y = 75^{°}, ∠ z = 70^{°}, ∠ w = 145^{°}$ .

In the figure, $l ∥ m$ . Find the values of $x, y, z, w$

.

Important Questions on Pairs of Angles and Parallel Lines

Learn and Prepare for any exam you want !

In the figure, l∥m. Find the values of x, y, z, w .

Important Questions on Pairs of Angles and Parallel Lines

Learn and Prepare for any exam you want !

In the figure, $l ∥ m$ . Find the values of $x, y, z, w$

.