Given:
In the given figure, [tex]m\angle 1=(3x+12)^\circ, m\angle 2=(3x+18)^\circ, m\angle 3=(7x+10)^\circ[/tex].
To find:
The measure of angle 3.
Solution:
According to the exterior angle theorem of a triangle, the measure of exterior angle is equal to the sum of two opposite interior angles of a triangle.
Using exterior angle theorem of a triangle, we get
[tex]m\angle 3=m\angle 1+m\angle 2[/tex]
[tex]7x+10=(3x+12)+(3x+18)[/tex]
[tex]7x+10=6x+30[/tex]
[tex]7x-6x=30-10[/tex]
[tex]x=20[/tex]
The value of x is 20. So, the measure of angle 3 is:
[tex]m\angle 3=(7x+10)^\circ[/tex]
[tex]m\angle 3=(7(20)+10)^\circ[/tex]
[tex]m\angle 3=(140+10)^\circ[/tex]
[tex]m\angle 3=150^\circ[/tex]
Therefore, the measure of angle 3 is 150 degrees.
