Answer:
[tex]m\angle D = 61\textdegree[/tex]
Step-by-step explanation:
In a parallelogram, opposite angles are congruent, so they have the same measure by the definition of congruence. Therefore, [tex]\angle B \cong \angle D[/tex], so [tex]m\angle B = m\angle D[/tex]. We are given the measures of these two angles, so we can write the following equation to solve for [tex]x[/tex]:
[tex]4x+9=6x-17[/tex]
Solving for [tex]x[/tex], we get:
[tex]4x+9=6x-17[/tex]
[tex]-2x+9=-17[/tex] (Subtract [tex]6x[/tex] from both sides of the equation)
[tex]-2x=-26[/tex] (Subtract [tex]9[/tex] from both sides of the equation to isolate [tex]x[/tex])
[tex]x=13[/tex] (Divide both sides of the equation to get rid of [tex]x[/tex]'s coefficient)
Therefore, [tex]m\angle D = 6x-17=6*13-17=78-17=61\textdegree[/tex].
Hope this helps!
