Find the value of the variable for which ABCD must be a parallelogram.

Question

Find the value of the variable for which ABCD must be a parallelogram. <A (3x+10)  <B (8x+5)

jdoe0001 · Answer

in a parallelogram the 2 pairs of sides will be parallel to one another
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so as you can see, they will also make 2 pairs of equal angles
so there'll be 2 angles equal to each other
and 2 more angles equal to each other

since in this case $\bf \angle A = 3x+10\
\angle B = 8x +5$
when A = B, you'd have 2 angles equal to each other
and thus the other 2 angles will also be equal

jdoe0001 · Answer

so just make $\bf 3x+10= 8x +5$
and solve for "x"