m∠1=29
In this question,
1) Since we have, vertical angles, whose measure are written as polynomials then we can write according to the Vertical angles theorem:
3y² + 2y – 10 =2y² + 7y + 4
3y²-2y² -7y+2y-10-4=0
y²-5y-14=0
1.1) Finding the roots by Sum and Product
S(x) = ___ +___ = -5
P(x) =____ x ___ = -14
x1=-2 or 7
Since our Domain, cannot allow negative numbers, let's keep the positive one 7
2) Moreover to that, m∠1 + 2y² + 7y + 4 = 180º
m∠1 +2(7)²+7(7)+4=180
m∠1 +151 =180
m∠1=180-151
m∠1=29
