Find the measure of each angle

Explanation

We will use the fact that the sum of the angle measures of any triangle is 180° to write an equation that models the situation. We can then solve the equation to find the unknown angle measure , and use it to evaluate the expression \(2x\) and \(x + 32^o\) 

• The sum of the angle measures of any triangle is 180^o
  • \(x + 32^o + x + 2x = 180^o\)
• Combine like terms: x + x + 2x = 4x
  • \(4x + 32^o = 180^o\)
• To isolate the variable term, 4x subtract 32^o from both sides
  • \(4x + 32^o - \color{red}{32^o} = 180^o - \color{red}{32^o}\)
• Do the subtraction
  • \(4x = 148^o\)
• To isolate x, divide both sides by 4
  • \(\frac{4x}{\color{red}{4}} = \frac{148^o}{\color{red}{4}}\)
• Do the division.  This is the measure of ∠B