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<a = 90°                              (right angle)

<b = 90°  - 59°  = 31°          (complementary angles)

<c = 180°  - 59°  = 121°        (supplementary angles)

<d = 59°                              (vertical angles)

a =90

b = 31

c = 121

d =59

Step-by-step explanation:

Angle a is a right angle = 90 degrees.  The corner box means that it equals 90 degrees

a = 90

Angles b and 59 are complementary

The equal 90 degrees since angle a is a right angle and the three angles make a straight line

a+b+ 59 = 180 and a is 90

so b+59 = 90  (which means they are complementary)

Subtract 59 from each side

b+59-59 = 90-59

b = 31

Angle c and 59 are supplementary

They form a straight line or 180

c+59 = 180

Subtract 59 from each side

c+59-59= 180-59

c =121

Angle c and d are complementary  (they form a straight line)

c+d = 180

Since c is 121

121+d = 180

Subtract 121 from each side

121-121+d =180-121

d = 59

there are infinitely many solutions.