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Answer :
The numerical sum of ∠DEA and ∠AEB is 180°.
Numerical value of x is 14.5°.
Measure of ∠DEA is 39.5°.
Measure of ∠AEB is 140.5°.
What is Supplementary angles?
- If the sum of two linear angles is 180° then, they are known as supplementary angles.
- ∠A + ∠B = 180°, (∠A and ∠B are linear angles.)
Given: Two lines intersect.
Points D, E and B lie on a horizontal line and point E is intersected by line AC.
∠DEA = x + 25
∠AEB = 9x + 10
Now, from the given information we can deduce that to obtain the angles ∠AED and ∠AEB, point E should lie in between points D and B.
Since, points D, E and B lie on the horizontal line, then the ∠DEA and ∠AEB should form the supplementary angles (Figure 1).
⇒ ∠DEA + ∠AEB = 180°
⇒ (x + 25) + (9x + 10) = 180°
⇒ 10x + 35° = 180°
⇒ 10x = 145°
⇒ x = 14.5°
Now, we will substitute the value of x = 14.5° in the ∠DEA and ∠AEB, hence we get:
⇒ ∠DEA = x + 25°
⇒ ∠DEA = 14.5° + 25°
⇒ ∠DEA = 39.5°
Also,
⇒ ∠AEB = 9x + 10°
⇒ ∠AEB = 9 × 14.5° + 10°
⇒ ∠AEB = 130.5° + 10°
⇒ ∠AEB = 140.5°
Therefore, the numerical sum of the degree measures of ∠DEA and ∠AEB is 180°; The numerical measures of the angles is, x = 14.5°, m∠DEA = 39.5° and m∠AEB = 140.5°.
Learn more about the Supplementary angles here: https://brainly.com/question/13045673?referrer=searchResults
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Rewritten by : Jeany
Answer:
What is the numerical sum of the degree measures of ∠DEA and ∠AEB?
180
What are the numerical measures of the angles?
x = 14.5
m∠DEA = 39.5°
m∠AEB = 140.5°
Step-by-step explanation:
x + 25 + 9x + 10 = 180
Subtract 35 from both sides and you get,
10x = 145
The divide both sides by 10 and you get,
x = 14.5
To get the angle measurements you plug x back into the angle equations which in this case is 14.5.
It would look like,
m∠DEA = (14.5 + 25) = 39.5
and,
m∠AEB = (9 (14.5) + 10) = 140.5
