Question

How do I find x and the measure for angle B and the measure of angle C

Answer 1

9514 1404 393

Answer:

• x = 3
• ∠B = 70°
• ∠C = 50°

Step-by-step explanation:

The useful relation for this problem is ...

   an exterior angle is equal to the sum of the remote interior angles

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This means ...

  120° = (15x+5)° +(22x+4)°

  120 = 37x +9 . . . . . collect terms, divide by °

  111 = 37x . . . . . . . . . subtract 9

  3 = x . . . . . . . . . . . . divide by 37

Then the angle measures are ...

  ∠B = (22x +4)° = (22·3 +4)° = 70°

  ∠C = (15x +5)° = (15·3 +5)° = 50°