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°

answer is x<

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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