Question 1114061
.
Parallelogram ABCD with m < B = 5x and m < C = 3x+4. How do I find the number of degree in < D?
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<pre>
There is nothing easier.


The angles B and C are consecutive angles of the parallelogram.


Consecutive angles of any parallelogram are supplementary. It means that they sum up to 180 degrees.

It gives you an equation


5x + (3x+4) = 180.


5x + 3x + 4 = 180

8x = 180-4 = 176  ====>  x = {{{176/8}}} = 22.


Therefore,  angle B is 5*22 = 110.


In parallelogram ABCD, the angles B and D are opposite angles.

In any parallelogram, the opposite angles are congruent.


Therefore, the measure of the angle D is the same as for angle B, i.e. 110 degrees.
</pre>

Solved.


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To see other similar solved problems, look into the lessons

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&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Points-lines-and-rays/Solved-problems-on-angles-of-a-parallelogram.lesson>Solved problems on angles of a parallelogram</A> (*)

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&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Points-lines-and-rays/Solved-problems-on-angles-of-a-polygon.lesson>Solved problems on angles of a polygon</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Points-lines-and-rays/Solved-problems-on-missed-angle-of-a-polygon.lesson>Solved problems on missed angle of a polygon</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Points-lines-and-rays/Solved-problems-on-angles-of-a-regular-polygon.lesson>Solved problems on angles of a regular polygon</A>

in this site. 


The most relevant lesson is marked (*) in this list.


Also, &nbsp;you have this free of charge online textbook on Geometry

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson>GEOMETRY - YOUR ONLINE TEXTBOOK</A> 

in this site.


The referred lessons are the part of this online textbook under the topic &nbsp;"<U>Finding angles of triangles, parallelograms and rectangles</U>".



Save the link to this online textbook together with its description


Free of charge online textbook in GEOMETRY
https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson


to your archive and use it when it is needed.