COMPLEMENTARY SUPPLEMENTARY AND ANGLE AT CENTRE

Complementary angles :

Two angles are complementary, if the sum of their measures is equal to 90. 

Supplementary angles :

Two angles are supplementary angles if the sum of their measures is equal to 180 degrees.

Angle at center :

Angle at the center is 360 degree.

Find the size of the unknown angle in:

Problem 1 :

Solution:

In the picture above, the angles x° and 65° are complementary.

x + 65° = 90°

x = 90° - 65°

x = 25°

Problem 2 :

Solution:

In the picture above, the angles y° and y° are complementary.

y° + y° = 90°

2y = 90°

y = 45°

Problem 3 :

Solution:

In the picture above, the angles a°, a° and a° are complementary.

a° + a° + a° = 90°

3a = 90°

a = 30°

Problem 4 :

Solution:

In the picture above, the angles n° and 73° are supplementary.

n° + 73° = 180°

n = 180° - 73°

n = 107°

Problem 5 :

Solution:

In the picture above, the angles 45°, p° and 85° are supplementary.

45° + p° + 85° = 180°

130° + p = 180° 

p = 180° - 130°

p = 50°

Problem 6 :

Solution:

In the picture above, the angles x°, x° and x° are supplementary.

x° + x° + x° = 180°

3x = 180°

x = 60°

Problem 7 :

Solution:

90° + 72° + 86° + g° = 360°

248° + g = 360°

g = 360° - 248°

g = 112°

Problem 8 :

Solution:

80° + 90° + h° + h° = 360°

170° + 2h = 360°

2h = 360° - 170°

2h = 190°

h = 95°

Problem 9 :

Solution:

60° + i° + 56° + 110° + i° = 360°

226° + 2i = 360°

2i = 360° - 226°

2i = 134°

i = 67°