1) what is the numerical sum of the degree measures of ∠dea and ∠aeb? (90,180,360)
2) what are the numerical measures of the angles?
x = __ (14.5,18,21.5)
m∠dea = ° (39.5,43,140.5)
m∠aeb = ° (39.5,140.5,172)

the parentheses are the options for the answer.

The value of x,  ∠DEA, and ∠AEB are 14.5, 39.5, and 140.5 degrees

Supplementary angles are angles that sum up to 180degrees

From the given diagram, we can see that:

m<DEA + m<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 degrees

Get ∠AEB:

∠AEB = 9x+10

∠AEB = 9(14.5) + 10

∠AEB = 130.5 + 10

∠AEB = 140.5 degrees

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

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x = 14.5°

∠DEA = 39.5°

∠AEB = 140.5°

Step-by-step explanation:

Finding x:

We are to find the value of x. We know that the sum of supplementary angles on a straight line is 180°. Therefore, we can write it as:

x +25 + 9x + 10 = 180

10x + 35 = 180

10x = 180 - 35

x = 145/10

x = 14.5°

Finding ∠DEA:

∠DEA = x + 25° = 14.5 + 25

∠DEA = 39.5°

Finding ∠AEB:

∠AEB = 9x + 10 = 9(14.5) + 10

∠AEB = 140.5°

d

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