Question

The rhombus QRST is made of two congruent isosceles triangles. Given angle QRS = 34, what is the measure of angle S?

Answer 1

Answer:

146

Step-by-step explanation:

Since we know that this is a rhombus, we know that opposite angles must be equal to each other. This means that angle QTS is equal to angle QRS. Therefore angle QTS also equals 34.

Now, we also know that all the interior angles in a quadrilateral add up to 360. We can subtract 360-34-34=292.

Now we know that the remaining two angles S and Q need to add up to 292. We also know that they are equal because they are opposite angles. Therefore, we can solve the equation 292÷2=146. Each of these angles is 146. So the measure of angle S is 146.

Answer 2

The measure angle of S is 146 .

A rhombus is a special case of the parallelogram and is a quadrilateral with four equal sides. In a rhombus, the opposite sides are parallel and the opposite angles are equal. Also, all the sides of the rhombus are equal in length and the diagonals bisect each other at right angles. The rhombus is also known as a diamond.

By symmetry ;

This means that m∠QTS is equal to m∠QRS. Therefore ∠QTS is also equals 34.

We also know that The common property for all the above four-sided shapes is the sum of interior angles is always equal to 360 degrees. For a regular quadrilateral such as square, each interior angle will be equal to: 360/4 = 90 degrees.

Now we know that the remaining two angles S and Q need to add up to 292.

= 360 -34 -34= 292

We also know that they are equal because they are opposite angles.

Therefore, we can solve the equation,

$\frac{sum of two opposite angle}{2}$ = $\frac{292}{2}$ = 146

Each of these angles is 146.

So the measure of angle S is 146.

For the more information about properties of rhombus click the link given below.

https://brainly.com/question/4115340