Question

What is the numerical sum of the degree measures of
2DEA and ZAEB?
What are the numerical measures of the angles?
(x + 25)
(9x + 10)
m2DEA=
MZAEB
FO
First drop down choices are: 90, 180, 360
2nd drop down:
14.5, 18, 21.5
3rd drop down:
39.5, 43, 140.5
Last drop down:
39.5, 140.5, 172

Answer 1

The numerical sum of the degree measures of ∠DEA and ∠AEB is 180°.

x = 14.5

m∠DEA = 39.5°

m∠AEB = 140.5°

Solution:

Sum of the measures of adjacent angles in a straight line is 180°.

m∠DEA + m∠AEB = 180°

The numerical sum of the degree measures of ∠DEA and ∠AEB is 180°.

⇒ m∠DEA + m∠AEB = 180°

⇒ (x + 25)° + (9x + 10)° = 180°

⇒ x° + 25° + 9x° + 10° = 180°

⇒ 10x° + 35° = 180°

Subtract 35° from both sides of the equation.

⇒ 10x° = 145°

⇒ x° = 14.5°

⇒ x = 14.5

m∠DEA = (9x + 10)°

             = (9(14.5) + 10)°

m∠DEA = 39.5°

m∠AEB = (x + 25)°

             = (14.5 + 25)°

m∠AEB = 140.5°