Question

In parallelogram ABCD, the measure of angle A = 3x and the measure of angle B = x + 10.

Answer 1

`D = 52.5`

Step-by-step explanation:

See attachment for diagram

Given

`A = 3x`

`B = x + 10`

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.

`A + B = 180`

Substitute values for A and B

`3x + x +10 = 180`

`4x +10 = 180`

Collect Like Terms

`4x = 180 - 10`

`4x = 170`

Solve for x

`x = 170/4`

`x = 42.5`

Also from the attachment,

D is at opposite of B

And opposite angles of a parallelogram are equal

i.e.

`D = B = x + 10`

`D = x + 10`

Substitute 42.5 for x

`D = 42.5 + 10`

`D = 52.5`