Question

1. what is the value of y? 8.7 8 4.7 4

Explanation:

Step1: Identify vertical angles

$\angle AED = \angle BEC$ (vertical angles are equal)
$\angle BEC = 42^\circ + 38^\circ = 80^\circ$
So $\angle AED = 80^\circ$

Step2: Set up equation for $\angle AED$

$\angle AED = (6y + 14)^\circ$
$6y + 14 = 80$

Step3: Solve for y

$6y = 80 - 14 = 66$
$y = \frac{66}{6} = 11$? Wait, no—wait, correction: Wait, $\angle AED$ is the angle at E between A and D, which equals the sum of angles at E from B and C? Wait no, actually, $\angle AEB$ and $\angle CED$ are vertical angles? Wait no, let's recheck: The angles at E: $\angle AED$ and $\angle BEC$ are vertical angles. $\angle BEC = 42^\circ + 38^\circ = 80^\circ$, so $\angle AED = 80^\circ$. Then $6y +14 =80$ → $6y=66$ → $y=11$? But 11 isn't an option. Wait, maybe $\angle AED$ is supplementary? No, wait the options include 8: Let's try $6y+14=62$? No, wait maybe $\angle AED = 6y+14$ and $\angle BEC = 42+38=80$, but if they are vertical angles, 6y+14=80→y=11 (not option). Wait maybe $\angle AED$ is equal to $\angle ABC$? No, $\angle ABC=42$, so 6y+14=42→6y=28→y≈4.7 (option C). Oh! Maybe $\angle ADB = \angle ACB$ (same arc AB). $\angle ACB=38$, so 6y+14=38→6y=24→y=4 (option D). Wait $\angle ADB$ and $\angle ACB$ subtend arc AB: yes! Inscribed angles subtended by the same arc are equal. So $\angle ADB = \angle ACB =38^\circ$. So $6y+14=38$ → $6y=24$ → $y=4$.

Answer:

D. 4