(In the picture, QRST looks like a rhombus, so I will assume that it is a rhombus.)
In a rhombus, opposite angles are congruent based on the alternate interior angle theorem. In other words, R and T along with Q and S are both alternate interior angle pairs.
(You can actually test this by printing out a rhombus, cutting out the angles, and matching up the opposite ones.)
We know that Q is equal to 4x + 10, but we need to solve for x. Since Q and S are congruent, we can set them equal to each other:
1) 4x + 10 = 5x - 3
2) 4x + 13 = 5x
3) 5x = 4x + 13
4) x = 13
Now let's plug 13 in for Q:
5) 4(13) + 10 = 52+10 = 62
I got m<Q = 62 degrees. Hope this helps!
The area of a polygon equals
area = circumradius² * number of sides * sin (360 / # of sides) / 2
area = 77² * 20 * sin (360 / 20) / 2
area = 77² * 20 * sin (18) / 2
area = 118,580 * 0.30902 / 2
area =
<span>
<span>
<span>
36,643.59
</span>
</span>
</span>
/ 2
area =
18,321.8 square millimeters
They are Vertical Angles as they are directly across from one another.
I’m pretty sure it’s irrational
