Answer:
[tex]\huge\boxed{\sf 126\° \ OR \ 145 \°}[/tex]
Step-by-step explanation:
m∠4 + m∠7 = 180 (Adjacent Angles of a parallelogram)
Given that m∠4 = x + 45, m∠7 = x² + 45
x + 45 + x² + 45 = 180
x² + x + 90 = 180
x² + x = 180 - 90
x² + x = 90
x² + x - 90 = 0
Using mid-term break formula
x² + 10x - 9x - 90 = 0
x(x+10) - 9(x+10) = 0
(x - 9)(x + 10) = 0
Either,
x-9 = 0 OR x+10 = 0
x = 9 OR x = -10
[tex]\rule[225]{225}{2}[/tex]
Now,
m < 7 = x² + 45
For x = 9
m < 7 = (9)² + 45
m < 7 = 81 + 45
m < 7 = 126°
For x = -10
m < 7 = (-10)² + 45
m < 7 = 100 + 45
m < 7 = 145°
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AnonymousHelper1807
