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ZA and B are complementary angles. If mZA= (x + 9)° and m ZB = (72 – 15)°, then find the measure of ZB.

User DelusionaL
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Final answer:

To find the measure of ZB, we solve for x using the property of complementary angles summing up to 90 degrees. Plugging x back into the expression for ZB, we calculate that the measure of ZB is 63°.

Step-by-step explanation:

The question involves finding the measure of angle ZB, given that angles ZA and ZB are complementary angles and their measurements in terms of x are provided. When two angles are complementary, their measures add up to 90 degrees. The measure of angle ZA is given as (x + 9)° and the measure of angle ZB is (72 - x)°, as 15 was subtracted from 72.

To find x, we use the fact that the sum of the measures of complementary angles is 90°:

  • m∠ZA + m∠ZB = 90°
  • (x + 9)° + (72 - x)° = 90°
  • x + 9 + 72 - x = 90
  • 81 = 90
  • x = 90 - 81
  • x = 9

Now that we have the value of x, we can find the measure of ZB by plugging x back into the expression for m∠ZB:

  • m∠ZB = (72 - x)°
  • m∠ZB = (72 - 9)°
  • m∠ZB = 63°

Therefore, the measure of ZB is 63°.

User Andreas Ka
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