Answer:
A. 100 degrees
Step-by-step explanation:
Given:
[tex] m\angle ABC = 3y + 5 [/tex]
[tex] m\angle ADC = 5y - 45 [/tex]
Required:
[tex] m\angle BCD [/tex]
SOLUTION:
✍️First, create an equation that you will use to find the value of y.
[tex] m\angle ABC = m\angle ADC [/tex] (opposite angles of a parallelogram are congruent to each other)
[tex] 3y + 5 = 5y - 45 [/tex] (substitution)
Collect like terms
[tex] 3y - 5y = -5 - 45 [/tex]
[tex] -2y = -50 [/tex]
Divide both sides by -2
[tex] y = 25 [/tex]
✍️Next, find [tex] m\angle ABC [/tex] and [tex] m\angle ADC [/tex].
[tex] m\angle ABC = 3y + 5 [/tex]
Plug in the value of y
[tex] m\angle ABC = 3(25) + 5 = 75 + 5 = 80 [/tex]
[tex] m\angle ADC = 5y - 45 [/tex]
Plug in the value of y
[tex] m\angle ADC = 5(25) - 45 = 125 - 45 = 80 [/tex]
✍️Next, find [tex] m\angle BCD [/tex].
[tex] m\angle BCD + m\angle ADC = 180 [/tex] (consecutive angles in a parallelogram are supplementary)
[tex] m\angle BCD + 80 = 180 [/tex] (substitution)
Subtract 80 from each side
[tex] m\angle BCD = 180 - 80 [/tex]
✅[tex] m\angle BCD = 100 [/tex]
