Answer
The pair of complementary angles is \[\measuredangle 1\]and\[\measuredangle 5\].
Work Step by Step
It is known that two angles are said to be complementary when the sum of two angles is equal to 90°.
Now the pairs of angles in the figure that are complementary are as follows:
\[\measuredangle 1\]and\[\measuredangle 2\], \[\measuredangle 4\] and \[\measuredangle 5\]and\[\measuredangle 4\], \[\measuredangle 1\] and \[\measuredangle 5\]and\[\measuredangle 2\]and\[\measuredangle 4\].
The sum of \[\measuredangle 1\] and \[\measuredangle 2\] will be 90°as \[\measuredangle 1\], \[\measuredangle 2\] and \[\measuredangle 3\] constitutes a straight line the sum of which is 180°.
Now the sum of \[\measuredangle 1\] and \[\measuredangle 2\] will be as follows:
\[\begin{align}
& \measuredangle 1+\measuredangle 2+\measuredangle 3=180{}^\circ \\
& \measuredangle 1+\measuredangle 2+90{}^\circ =180{}^\circ \\
& \measuredangle 1+\measuredangle 2=90{}^\circ
\end{align}\]
Thus, sum of\[\measuredangle 1\] and \[\measuredangle 2\] is 90°.
Similarly, the sum of \[\measuredangle 4\] and \[\measuredangle 5\] will be as follows:
\[\begin{align}
& \measuredangle 4+\measuredangle 5+\measuredangle 6=180{}^\circ \\
& \measuredangle 4+\measuredangle 5+90{}^\circ =180{}^\circ \\
& \measuredangle 4+\measuredangle 5=180{}^\circ -90{}^\circ \\
& =90{}^\circ
\end{align}\]
Thus, the sum of \[\measuredangle 4\] and \[\measuredangle 5\] is 90°
Similarly, the sum of \[\measuredangle 2\] and \[\measuredangle 4\]will be as follows:
\[\begin{align}
& \measuredangle 2+\measuredangle 3+\measuredangle 4=180{}^\circ \\
& \measuredangle 2+90{}^\circ +\measuredangle 4=180{}^\circ \\
& \measuredangle 2+\measuredangle 4=180{}^\circ -90{}^\circ \\
& \measuredangle 2+\measuredangle 4=90{}^\circ
\end{align}\]
In the same manner the sum of \[\measuredangle 1\] and \[\measuredangle 5\] will be as follows:
\[\begin{align}
& \measuredangle 1+\measuredangle 5+\measuredangle 6=180{}^\circ \\
& \measuredangle 1+\measuredangle 5+90{}^\circ =180{}^\circ \\
& \measuredangle 1+\measuredangle 5=180{}^\circ -90{}^\circ \\
& =90{}^\circ
\end{align}\]
\[\measuredangle 1\]and\[\measuredangle 5\] are complimentary angles. Thus, option d seems to be the correct choice and rest options are in correct.
