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The measure of the angles of a quadrilateral are x, x+15, x+25, and x+20 degrees. Find the measure of each angle of ABCD.

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MIKUROSONYAIN

QUESTION: The measure of the angles of a quadrilateral are x, x+15, x+25, and x+20 degrees. Find the measure of each angle of ABCD.

ANSWERS:

  • m∠A = 75
  • m∠B = 90
  • m∠C = 100
  • m∠D = 95

  • Add the measures of all the angles.
  • x + x + 15 + x + 25 + x + 20 = 4x + 60

  • Make an equation. (360 is the sum of interior angles of quadrialateral)
  • 4x + 60 = 360

  • Solve using SPE and DPE (Subtraction Porperty of Equality and Division Property of Equality, respectively)
  • 4x + 60 - 60 = 360 - 60
  • 4x + 300
  • [tex]\frac{4x}{4}[/tex] = [tex]\frac{300}{4}[/tex]
  • x = 75
  • The 60 gets cancelled out due to Inverse Property of Addition.

  • Substitute the answer to x in the measures of all angles.
  • m∠A = 75
  • m∠B = 75 + 15 = 90
  • m∠C = 75 + 25 = 100
  • m∠D = 75 + 20 = 95

  • Let me double check to make sure our answers are correct. To do this, add all our answers to see if their sum is 360.
  • 75 + 90 + 100 + 95 = 360
  • CORRECT!

=) hope this helps

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