Question 199233
Let x be the first angle, then (90-x) is the measure of the second angle, because the sum of these two complementary angles is 90 degrees.
{{{x+(90-x) = 90}}}
The problem states that the sum of the first angle (x) and one fourth of the second angle ({{{(1/4)(90-x)}}}) is 75 degrees, so you can write the equation to find x.
{{{x+(1/4)(90-x) = 75}}} Multiply through by 4 to clear the fraction.
{{{4x+(90-x) = 300}}} Simplfy the left side.
{{{3x+90 = 300}}} Subtract 90 from both sides.
{{{3x = 210}}} Finally, divide both sides by 3.
{{{x = 70}}}degrees, and...
{{{90-x = 20}}}degrees.
Check:
{{{x+(1/4)(90-x) = 75}}} Substitute x = 70.
{{{70+(1/4)(90-70) = 75}}}
{{{70+(1/4)(20) = 75}}}
{{{70+5 = 75}}}
{{{75 = 75}}}