Name: Understanding Vertically Opposite Angles
Uploaded: 2019-07-19
Duration: 6 min 7 s
Description: Did you know that many examples of vertically opposite angles can be seen in our daily lives? A railroad crossing sign for example. So how do we define this...

Question

In Figure, line $l ∥ m$ and $n$ is a transversal. If $∠ 1 = 40 °$ , find all the angles and check that all corresponding angles and alternate angles are equal.

Accepted Answer

Given figure:

Given $l ∥ m$ , line $n$ is a transversal.

Also $∠ 1 = 40 °$

Here $∠ 1 = ∠ 3 = 40 °$ (Vertically opposite angles)

$∠ 1 + ∠ 2 = 180 ° \Rightarrow ∠ 2 = 180 ° - ∠ 1 = 180 ° - 40 ° = 140 °$ (Linear pair of angles are supplementary)

$∠ 1 + ∠ 4 = 180 ° \Rightarrow ∠ 4 = 140 °$ (Linear pair of angles are supplementary)

$∠ 4 + ∠ 5 = 180 ° \Rightarrow ∠ 5 = 40 °$ (Co-interior angles are supplementary)

$∠ 5 = ∠ 7 = 40 °$ (Vertically opposite angles)

$∠ 5 + ∠ 6 = 180 ° \Rightarrow ∠ 6 = 140 °$ (Linear pair of angles are supplementary)

$∠ 6 = ∠ 8 = 140 °$ (Vertically opposite angles)

Therefore, the remaining angles are $∠ 2 = 140 °, ∠ 3 = 40 °, ∠ 4 = 140 °, ∠ 5 = 40 °, ∠ 6 = 140 °, ∠ 7 = 40 °, ∠ 8 = 140 °$ .

Corresponding angles:

$∠ 1 = ∠ 5 = 40 °, ∠ 2 = ∠ 6 = 140 °, ∠ 4 = ∠ 8 = 140 °, ∠ 3 = ∠ 7 = 40 °$

Alternate angles:

$∠ 3 = ∠ 5 = 40 °, ∠ 6 = ∠ 4 = 140 °, ∠ 1 = ∠ 7 = 40 °, ∠ 2 = ∠ 8 = 140 °$

Hence, verified.

In Figure, line $l ∥ m$ and $n$ is a transversal. If $∠ 1 = 40 °$ , find all the angles and check that all corresponding angles and alternate angles are equal.

Important Questions on Lines and Angles

Learn and Prepare for any exam you want !

In Figure, line l∥m and n is a transversal. If∠1=40°, find all the angles and check that all corresponding angles and alternate angles are equal.

Important Questions on Lines and Angles

Learn and Prepare for any exam you want !

In Figure, line $l ∥ m$ and $n$ is a transversal. If $∠ 1 = 40 °$ , find all the angles and check that all corresponding angles and alternate angles are equal.