Answer
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Hint: In trapezium, the sum of two adjacent angles made by parallel lines is ${180^ \circ }$. Use this theorem for the pair of angles made by parallel sides and find the required angles.
Complete step by step answer:
From the above figure, ABCD is a trapezium in which AB is parallel to DC and we have:
$ \Rightarrow \angle A = \angle B = {40^ \circ }.$
We know that, in trapezium, the sum of two adjacent angles made by parallel lines is ${180^ \circ }$. Thus, according to this rule, we have:
$ \Rightarrow \angle A + \angle D = {180^ \circ }$ (sum of interior angle on the same side of the transversal is ${180^ \circ }$)
$
\Rightarrow \angle D = {180^ \circ } - \angle A \\
\Rightarrow \angle D = {180^ \circ } - {40^ \circ } \\
\Rightarrow \angle D = {140^ \circ } \\
$
Similarly for other two angles:
$
\angle B + \angle C = {180^ \circ } \\
\Rightarrow {40^ \circ } + \angle C = {180^ \circ } \\
\Rightarrow \angle C = {140^ \circ } \\
$
Hence the measure of the other two angles is ${140^ \circ }$ each.
Note: If in a trapezium, non-parallel sides are equal in length then in that case, the opposite angles of the trapezium will be supplementary to each other. And such trapezium is called isosceles trapezium.
Complete step by step answer:
From the above figure, ABCD is a trapezium in which AB is parallel to DC and we have:
$ \Rightarrow \angle A = \angle B = {40^ \circ }.$
We know that, in trapezium, the sum of two adjacent angles made by parallel lines is ${180^ \circ }$. Thus, according to this rule, we have:
$ \Rightarrow \angle A + \angle D = {180^ \circ }$ (sum of interior angle on the same side of the transversal is ${180^ \circ }$)
$
\Rightarrow \angle D = {180^ \circ } - \angle A \\
\Rightarrow \angle D = {180^ \circ } - {40^ \circ } \\
\Rightarrow \angle D = {140^ \circ } \\
$
Similarly for other two angles:
$
\angle B + \angle C = {180^ \circ } \\
\Rightarrow {40^ \circ } + \angle C = {180^ \circ } \\
\Rightarrow \angle C = {140^ \circ } \\
$
Hence the measure of the other two angles is ${140^ \circ }$ each.
Note: If in a trapezium, non-parallel sides are equal in length then in that case, the opposite angles of the trapezium will be supplementary to each other. And such trapezium is called isosceles trapezium.
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