Answer:
[tex]D = 52.5[/tex]
Explanation:
See attachment for diagram
Given
[tex]A = 3x[/tex]
[tex]B = x + 10[/tex]
Required
What is the measure of angle D? ------ Missing part of the question
From the attachment, we have that
A is adjacent to B
And adjacent angles of a parallelogram add up to 180.
i.e.
[tex]A + B = 180[/tex]
Substitute values for A and B
[tex]3x + x +10 = 180[/tex]
[tex]4x +10 = 180[/tex]
Collect Like Terms
[tex]4x = 180 - 10[/tex]
[tex]4x = 170[/tex]
Solve for x
[tex]x = 170/4[/tex]
[tex]x = 42.5[/tex]
Also from the attachment,
D is at opposite of B
And opposite angles of a parallelogram are equal
i.e.
[tex]D = B = x + 10[/tex]
[tex]D = x + 10[/tex]
Substitute 42.5 for x
[tex]D = 42.5 + 10[/tex]
[tex]D = 52.5[/tex]
