In the diagram, ABCD is a parallelogram. The diagonals of the parallelogram intersect at point T. HELP

Question

asked Mar 19, 2021 57.8k views

1 Answer

Jaecheol Park · Answer 1 · 2021-03-24T13:46:56+0000

Answer:

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

$m\angle BCD = 180 - 80$

✅
$m\angle BCD = 100$