Question

Geometry: Angle
d) If 2p° and (p + 15)° are a pair of complementary angles, find them.
e) If x° andare a pair of supplementary angles find them.
f) If pair of complementary angles are in the ratio 4:11, find them.
g) If a pair of supplementary angles are in the ratio 7:5, find them.​

Answer 1

Answer:

d) 2p° and (p+15) ° are complementary angles.

2p° + p° + 15° = 90°

3p° = 90° - 15°

p° = 75°/3

p = 25°

Now, 2p° = 2×25° = 50°

(p+15)° = 25°+15° = 40°

e) x° and x°÷4 are supplementary angles.

x° + x°÷4 = 180°

4x + x = 180°×4

5x = 180°×4

x = 180°×4/5

x° = 36° × 4 = 144°

And x°÷4 = 144/4 = 36°

f) Complementary angles in the ratio 4:11

Let the angles be 4x and 11x .

4x + 11x = 90°

15x = 90°

x = 6°

Now, 4x = 4×6 = 24°

11x = 11×6 = 66°

g) Supplementary angles in the ratio 7:5.

Let the angles be 7x and 5x.

7x + 5x = 180°

12x = 180°

x = 180°/12

x = 15°

Hence, 7x = 7×15 = 105°

5x = 5×15 = 75°.