All categories

2 years ago

Given that abcd is a rhombus, what is the value of x?

Mathematics

2 answers:

mrs_skeptik [129]2 years ago

6 0

Answer:

The answers is 19.5

Step-by-step explanation:

jeyben [28]2 years ago

4 0

Answer:

A - 19.5

Step-by-step explanation:

A Rhombus is characterized by the diagonals meeting at a right angle. Therefore, the angle in the center is 90 degrees.

If you look at the bottom triangle, you know that the angles of a triangle add up to 180 degrees. You can say that all of the angles of the triangle added to 180 are:

(3x + 12) + (x) +(90) = 180 degrees

4x + 102 = 180 degrees combining like terms

4x + 102 - 102 = 180 - 102

4x = 78

4x/4 = 78/4

x = 19.5 degrees

You might be interested in

Whats the answer can someone answer please

Rufina [12.5K]

Answer:

b and c

Step-by-step explanation:

6 0

3 years ago

Hi, teacher I was absent these days and I didn’t understand anything about this lesson and I need help this is not count as a te

motikmotik

Given:

There are given that the cos function:

$cos210^{\circ}=-\frac{\sqrt{3}}{2}$

Explanation:

To find the value, first, we need to use the half-angle formula:

So,

From the half-angle formula:

$cos(\frac{\theta}{2})=\pm\sqrt{\frac{1+cos\theta}{2}}$

Then,

Since 105 degrees is the 2nd quadrant so cosine is negative

Then,

By the formula:

$\begin{gathered} cos(105^{\circ})=cos(\frac{210^{\circ}}{2}) \\ =-\sqrt{\frac{1+cos(210)}{2}} \end{gathered}$

Then,

Put the value of cos210 degrees into the above function:

So,

$\begin{gathered} cos(105^{\circ})=-\sqrt{\frac{1+cos(210)}{2}} \\ cos(105^{\operatorname{\circ}})=-\sqrt{\frac{1-\frac{\sqrt{3}}{2}}{2}} \\ cos(105^{\circ})=-\sqrt{\frac{2-\sqrt{3}}{4}} \\ cos(105^{\circ})=-\frac{\sqrt{2-\sqrt{3}}}{2} \end{gathered}$

Final answer:

Hence, the value of the cos(105) is shown below: