Mathematics

Two complementary angles differ by $${6^ \circ }$$. Find the measure of 2 angles.


SOLUTION
Let the angles be x and y.
$$,x + y = {90^ \circ }\,\,\,\, - \left( i \right)$$
$$and\,\,\,\,\,\,\,\,\,\,x - y = {6^ \circ }\,\,\,\,\,\, - \left( {ii} \right)$$
$$Adding\,\,\left( i \right)\,\,and\,\,\left( {ii} \right),\,\,we\,get$$
$$\left( {x + y} \right) + \left( {x - y} \right) = {90^ \circ } + {6^ \circ }$$
$$2x = {96^ \circ }$$
$$x = {32^ \circ }$$
$$Putting\,\,this\,\,value\,\,in\,\left( i \right),\,\,we\,\,get$$
$${32^ \circ } + y = {90^ \circ }$$
$$y = {58^ \circ }$$
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