Question

∠5 is a supplement of ∠6, and m∠5=78°. Find m∠6.

Answer 1

`102^\circ`

Explanation:

Given that:

`\angle 5` is a supplement of
`\angle 6`.

m
`\angle 5` = 78°

To find:

m
`\angle 6` = ?

Solution:

First of all, let us learn about the concept of an angle being a supplement of the other angle.

`\angle B` is known as supplement of
`\angle A`, if sum of the two angles is equal to 180°.

`i.e. \angle A +\angle B=180^\circ`.

For example, angle made on one side by a line intersecting the other line are supplement of each other.

Here, we are given that
`\angle 5` is a supplement of
`\angle 6`.

In other words:

`\angle 5+\angle 6=180^\circ`

Putting value of
`\angle 5`:

`\Rightarrow 78^\circ+\angle 6=180^\circ\\\Rightarrow \angle 6 =180^\circ-78^\circ\\\Rightarrow \bold{\angle 6 =102^\circ\\}`

So, the answer is:
`102^\circ`