Answer:
x°= 30°, y°= 90°
Step-by-step explanation:
AB is a straight line. Thus, the sum of angles on AB is 180°. The abbreviation for this is (adj. ∠s on a str. line).
Let the point at the center be point E.
∠AEB +∠DEB= 180° (adj. ∠s on a str. line)
(y +x)° +(y -x)°= 180°
y +x +y -x= 180
2y= 180
y= 180 ÷2
y= 90
y°= 90°
∠AEC= ∠DEB (vert. opp. ∠s)
(2x)°= (y -x)°
2x= y -x
2x +x= y
3x= y (simplify)
3x= 90 (subst. y=90)
x= 90 ÷3
x= 30
x°= 30°
