Question

state whether the pair of angles given below are complementary or not.
(a) 55°, 35°
(b) 52°, 48°
(c) 45°, 45°
(d) 25°, 25°
the difference in the measures of two complementary angles is 12°. find the measures of the angles.
the difference in the measures of two supplementary angles is 80°. find the measures of the angles.

Explanation:

Step1: Recall complementary - angle definition

Complementary angles add up to 90°.

Step2: Check pair (a)

$55^{\circ}+35^{\circ}=90^{\circ}$, so they are complementary.

Step3: Check pair (b)

$52^{\circ}+48^{\circ}=100^{\circ}
eq90^{\circ}$, so they are not complementary.

Step4: Check pair (c)

$45^{\circ}+45^{\circ}=90^{\circ}$, so they are complementary.

Step5: Check pair (d)

$25^{\circ}+25^{\circ}=50^{\circ}
eq90^{\circ}$, so they are not complementary.

Answer:

(a) Complementary
(b) Not complementary
(c) Complementary
(d) Not complementary