Question

What are the numerical measures of the angles?

x =


m∠DEA = °


m∠AEB = °

Answer 1

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

°

Explanation:

Answer 2

ANSWER

The sum of m∠DEA and m∠AEB is 180°.

Reason: The sum of angles on a straight line is always 180°.


`(x + 25)+(9x + 10)=180 \degree`

Group like terms to get,


`x+9x=180-25-10`

Simplify, and get,


`10x = 145`

Divide both sides by 10 to get,


`x = 14.5`

We substitute this value to get the required angles.


`m \: ∠DEA=x+25`


`m \: ∠DEA = 14.5 + 25 = 39.5 \degree`


`m\:∠AEB=9x+ 10`


`m\:∠AEB = 9(14.5) + 10`


`m\: ∠AEB=130.5 + 10 = 140.5 \degree`