ANSWER
The sum of m∠DEA and m∠AEB is 180°.
Reason: The sum of angles on a straight line is always 180°.
[tex](x + 25)+(9x + 10)=180 \degree[/tex]
Group like terms to get,
[tex]x+9x=180-25-10[/tex]
Simplify, and get,
[tex]10x = 145[/tex]
Divide both sides by 10 to get,
[tex]x = 14.5[/tex]
We substitute this value to get the required angles.
[tex]m \: ∠DEA=x+25[/tex]
[tex]m \: ∠DEA = 14.5 + 25 = 39.5 \degree[/tex]
[tex]m\:∠AEB=9x+ 10[/tex]
[tex]m\:∠AEB = 9(14.5) + 10 [/tex]
[tex]m\: ∠AEB=130.5 + 10 = 140.5 \degree[/tex]
