PQRS is a parallelogram. If mQRS = (9x - 20)° and mSPQ = (4x + 90)°, what is the value of x?

22

8.5

14

10

x = 8.5

Step-by-step explanation:

In this question, we are to calculate the value of x.

To calculate this, we shall be utilizing one of the important properties of parallelogram.

This property is that opposite angles of a parallelogram are equal.

This means that mQSR = mSPQ = 4x + 90

Now to finally calculate x, we make use of another important parallelogram property which is that angles of parallelogram which faces each other are supplementary.

This means that they add up to be 180

Since mQSR faces mQRS

This means that;

4x + 90 + 9x -20 = 180

13x + 70 = 180

13x = 110

x = 110/13 which is approximately 8.5

4sqrt5

step-by-step explanation:

the base has dimensions of 8 x 4, so the diagonal is 64 + 16 square rooted or 4sqrt5.