Answer:
[tex]102^\circ[/tex]
Step-by-step explanation:
Given that:
[tex]\angle 5[/tex] is a supplement of [tex]\angle 6[/tex].
m[tex]\angle 5[/tex] = 78°
To find:
m[tex]\angle 6[/tex] = ?
Solution:
First of all, let us learn about the concept of an angle being a supplement of the other angle.
[tex]\angle B[/tex] is known as supplement of [tex]\angle A[/tex], if sum of the two angles is equal to 180°.
[tex]i.e. \angle A +\angle B=180^\circ[/tex].
For example, angle made on one side by a line intersecting the other line are supplement of each other.
Here, we are given that [tex]\angle 5[/tex] is a supplement of [tex]\angle 6[/tex].
In other words:
[tex]\angle 5+\angle 6=180^\circ[/tex]
Putting value of [tex]\angle 5[/tex]:
[tex]\Rightarrow 78^\circ+\angle 6=180^\circ\\\Rightarrow \angle 6 =180^\circ-78^\circ\\\Rightarrow \bold{\angle 6 =102^\circ\\}[/tex]
So, the answer is: [tex]102^\circ[/tex]
