Question

In the diagram, ABCD is a parallelogram. The

diagonals of the parallelogram intersect at point T.
HELP

Answer 1

A. 100 degrees

Explanation:

Given:

`m\angle ABC = 3y + 5`

`m\angle ADC = 5y - 45`

Required:

`m\angle BCD`

SOLUTION:

✍️First, create an equation that you will use to find the value of y.

`m\angle ABC = m\angle ADC` (opposite angles of a parallelogram are congruent to each other)

`3y + 5 = 5y - 45` (substitution)

Collect like terms

`3y - 5y = -5 - 45`

`-2y = -50`

Divide both sides by -2

`y = 25`

✍️Next, find
`m\angle ABC` and
`m\angle ADC`.

`m\angle ABC = 3y + 5`

Plug in the value of y

`m\angle ABC = 3(25) + 5 = 75 + 5 = 80`

`m\angle ADC = 5y - 45`

Plug in the value of y

`m\angle ADC = 5(25) - 45 = 125 - 45 = 80`

✍️Next, find
`m\angle BCD`.

`m\angle BCD + m\angle ADC = 180` (consecutive angles in a parallelogram are supplementary)

`m\angle BCD + 80 = 180` (substitution)

Subtract 80 from each side

`m\angle BCD = 180 - 80`

✅
`m\angle BCD = 100`