(a) Four angles of a quadrilateral are $$ 2 x, 4 x, 5 x $$ and $$ 7 x $$, find the angles in degreg (b) Four angles of a quadrilateral are in the ratio $$ 1: 2: 3: 3 $$, find the angles ine degree.

Question

UpStudy AI · Accepted Answer

(a) To find the angles of the quadrilateral, we first need to use the fact that the sum of the interior angles of any quadrilateral is $$ 360^\circ $$. We have the angles as $$ 2x, 4x, 5x, $$ and $$ 7x $$. So, we can set up the equation:

$$ 2x + 4x + 5x + 7x = 360^\circ $$

Combining like terms, we get:

$$ 18x = 360^\circ $$

Now, we solve for $$ x $$:

$$ x = \frac{360^\circ}{18} $$
$$ x = 20^\circ $$

Now we can find each angle:

$$ 2x = 2 \times 20^\circ = 40^\circ $$
$$ 4x = 4 \times 20^\circ = 80^\circ $$
$$ 5x = 5 \times 20^\circ = 100^\circ $$
$$ 7x = 7 \times 20^\circ = 140^\circ $$

So, the angles of the quadrilateral are $$ 40^\circ, 80^\circ, 100^\circ, $$ and $$ 140^\circ $$.

(b) For the second part, we are given that the angles are in the ratio $$ 1: 2: 3: 3 $$. Let's denote the common ratio as $$ r $$. So, the angles can be written as $$ r, 2r, 3r, $$ and $$ 3r $$. The sum of these angles is $$ 360^\circ $$, so we have:

$$ r + 2r + 3r + 3r = 360^\circ $$

Combining like terms, we get:

$$ 9r = 360^\circ $$

Now, we solve for $$ r $$:

$$ r = \frac{360^\circ}{9} $$
$$ r = 40^\circ $$

Now we can find each angle:

$$ r = 40^\circ $$
$$ 2r = 2 \times 40^\circ = 80^\circ $$
$$ 3r = 3 \times 40^\circ = 120^\circ $$
$$ 3r = 3 \times 40^\circ = 120^\circ $$

So, the angles of the quadrilateral are $$ 40^\circ, 80^\circ, 120^\circ, $$ and $$ 120^\circ $$.
(a) The angles of the quadrilateral are $$ 40^\circ, 80^\circ, 100^\circ, $$ and $$ 140^\circ $$. (b) The angles of the quadrilateral are $$ 40^\circ, 80^\circ, 120^\circ, $$ and $$ 120^\circ $$.

(a) Four angles of a quadrilateral are \( 2 x, 4 x, 5 x \) and \( 7 x \), find the angles in degreg (b) Four angles of a quadrilateral are in the ratio \( 1: 2: 3: 3 \), find the angles ine degree.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Bonus Knowledge

preguntas relacionadas

Latest Geometry Questions