With the markings on the triangle, we know that this is an isosceles triangle. This makes m∠B=m∠C.
Let x=m∠B. We know that all the angles in a triangle must add up to 180°
m∠A + m∠B + m∠C = 180
We know that m∠A=118°, m∠B=x, and m∠C=m∠B=x. Using this information, the equation changes to:
[tex]118+x+x=180[/tex]
[tex]2x+118=180[/tex]
Subtract both sides by 180
[tex]2x=62[/tex]
Divide both sides by 2
[tex]x=31[/tex]
Since x=31, m∠B must be 31°.
This explanation might be a bit confusing, so let me know if you need any clarifications, thanks!
~ Padoru
