Question

Determine the value of angle D in parallelogram ABCD​

Answer 1

• 61°

Explanation:

Opposite angles in parallelogram are congruent:

• 6x - 17 = 4x + 9
• 6x - 4x = 9 + 17
• 2x = 26
• x = 13

m∠D = 6*13° - 17° = 61°

Answer 2

`m\angle D = 61\textdegree`

Explanation:

In a parallelogram, opposite angles are congruent, so they have the same measure by the definition of congruence. Therefore,
`\angle B \cong \angle D`, so
`m\angle B = m\angle D`. We are given the measures of these two angles, so we can write the following equation to solve for
`x`:

`4x+9=6x-17`

Solving for
`x`, we get:

`4x+9=6x-17`

`-2x+9=-17` (Subtract
`6x` from both sides of the equation)

`-2x=-26` (Subtract
`9` from both sides of the equation to isolate
`x`)

`x=13` (Divide both sides of the equation to get rid of
`x`'s coefficient)

Therefore,
`m\angle D = 6x-17=6*13-17=78-17=61\textdegree`.

Hope this helps!