Two supplementary angles differ by 34. find the angles..

Mathematics

1 answer:

antiseptic1488 [7]2 years ago

3 0

Answer:

107°

73°

Step-by-step explanation:

Let the two supplementary angles be x° and y°.

x + y = 180....(1)

Since, supplementary angles differ by 34.

Therefore,

x - y = 34....(2)

Adding equations (1) & (2)

x + y = 180

x - y = 34

_________

2x = 214

x = 214/2

x = 107°

Plug x = 107 in equation (1)

107 + y = 180

y = 180- 107

y = 73°

You might be interested in

Let φ(x, y) = arctan (y/x) .

Alexandra [31]

Answer:

a) $\large F(x,y)=(-\frac{y}{x^2+y^2},\frac{x}{x^2+y^2})$

b) $\large \mathbb{R}^2-\{(0,0)\}$

c) the points of the form (x, -x) for x≠0

Step-by-step explanation:

If φ(x, y) = arctan (y/x), the vector field F = ∇φ would be

$\large F(x,y)=(\frac{\partial \phi}{\partial x},\frac{\partial \phi}{\partial y})$

On one hand we have,

$\large \frac{\partial \phi}{\partial x}=\frac{\partial arctan(y/x)}{\partial x}=\frac{-y/x^2}{1+(y/x)^2}=-\frac{y/x^2}{1+y^2/x^2}=\\\\=-\frac{y/x^2}{(x^2+y^2)/x^2}=-\frac{y}{x^2+y^2}$

On the other hand,

$\large \frac{\partial \phi}{\partial y}=\frac{\partial arctan(y/x)}{\partial y}=\frac{1/x}{1+(y/x)^2}=\frac{1/x}{1+y^2/x^2}=\\\\=\frac{1/x}{(x^2+y^2)/x^2}=\frac{x}{x^2+y^2}$