Answer:
Measurement of angle E is 55°.
Explanation:
By applying triangle sum theorem in ΔACE,
m∠A + m∠E + m∠C = 180°
(6x - 15)° + (4x)° + m∠E = 180°
m∠E = 180° - (10x - 15)
= (195 -10x)°
Similarly, in ΔBDE,
(5x - 1)° + (4x)° + m∠E = 180°
(9x - 1)° + m∠E = 180°
m∠E = 180 - (9x - 1)
= (181 - 9x)°
By equating both the measures of angle E,
(195 - 10x) = (181 - 9x)
195 - 181 = 10x - 9x
x = 14
m∠E = (195 - 10x) = 195 - 10(14)
= 195 - 140
= 55°
Therefore, measurement of angle E is 55°.