Question

An angle 4/5 of its supplement. What is its magnitudes.

Answer 1

Let angle be x.
x=4/5*(180-x)
5x=4(180-x)
5x=720-4x
9x=720
x=80
Therefore angle=80 degrees.
:)

Answer 2

Answer:

The magnitude of the angle having 4/5 of its supplement are $80^{\circ}, 100^{\circ}$.

To find:

The magnitude of the angle having 4/5 of its supplement

Solution:

Let the angle be $x^{\circ}$

Supplement of the angle =  $(180^{\circ}-x^{\circ})$

Given,

The angle is 4/5 of its supplement

$\begin{array} { c } { x ^ { \circ } = \frac { 4 } { 5 } \left( 180 ^ { \circ } - x ^ { \circ } \right) } \\\\ { 5 x ^ { \circ } = 4 \left( 180 ^ { \circ } - x ^ { \circ } \right) } \\\\ { 5 x ^ { \circ } = 4 \left( 180 ^ { \circ } )- 4 x ^ { \circ } \right. } \\\\ { 5 x ^ { \circ } + 4 x ^ { \circ } = 4 \times 180 ^ { \circ } } \\\\ { 9 x ^ { 0 } = 4 \times 180 ^ { \circ } } \\\\ { x ^ { \circ } = \frac { 4 \times 180 ^ { \circ } } { 9 } = 80 ^ { \circ } } \end{array}$

$\therefore \left( 180 ^ { \circ } - x ^ { \circ } \right) = 180 ^ { \circ } - 80 ^ { \circ } = 100 ^ { \circ }$

Hence, the magnitudes are $80 ^ { \circ } , 100 ^ { \circ }$