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What is the numerical sum of the degree measures of ∠DEA and ∠AEB?

Answer :

Answer:

The numerical sum of the degree measures of ∠DEA and ∠AEB is

= 180°

Step-by-step explanation:

supplementary angles :

The meaning of supplementary is related to angles that make a straight angle together. It means, two angles are said to be supplementary angles when they add up to 180 degrees. Two angles that are supplementary to each other, do not have to be next to each other. Two angles are supplementary, if

  • One of its angles is an acute angle and another angle is an obtuse angle.
  • Both of the angles are right angles.

This means that ∠p + ∠q = 180°.

From the given figure, we can see that:

∠DEA + ∠AEB = 180°

x+25+9x+10 = 180°

10x + 35 = 180°

10x = 180° - 35°

10x = 145°

x = 145/10

x = 14.5°

Get ∠DEA

∠DEA = x + 25

∠DEA = 14.5 +25

∠DEA = 39.5°

Get ∠AEB:

∠AEB = 9x+10

∠AEB = 9(14.5) + 10

∠AEB = 130.5 + 10

∠AEB = 140.5 °

Hence the value of x, ∠DEA, and ∠AEB are 14.5°, 39.5°, and 140.5°

so, The numerical sum of the degree measures of ∠DEA and ∠AEB is

= 39.5 + 140.5

= 180° (answer)

learn more about supplementary angles at

https://brainly.com/question/19281924

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