Answer:
First, my advice would be to make sure you know the rules of what makes a shape a certain shape. (ex. all angles add to 360, sides bisect each other, etc.) From there, you can look at the given shape and evaluate whether or not it is that shape. From there, you can solve for the different values with the knowledge of what they must be.
Here is how you would solve the first one:
We know that in order for a shape to be a parallelogram, the interior angles must add up to 360 degrees. We also know that opposite angles are equal. This problem states that the shape is indeed a parallelogram so we now know that these rules are true.
So, we can set up the equation: 2(3x + 5) + 2(9x - 17) = 360 and solve for x.
The reason we have that equation is as follows.
Angle Q is equal to (3x+5).
Since Angle S is opposite angle Q, we know that Angle S is also equal to (3x+5). Therefore we can multiply that equation by two which will be equal to those angles combined.
The same reasoning applies to Angles R and T. They are opposite which means they are congruent, so we can multiply (9x-17) by two in order to get the value of those two angles combined.
Finally, we will add them because all four angles will equal 360 degrees, so when we solve, we will get the value of x.
You can stop here for the answer to your question, but some questions will require you to both solve for x and find the value of each angle. So that is what the next step explains.
Once you have the value of x, plug it into the two equations we started with to get the angle values for Angle Q and T. Remember, the angle values for Q is also the angle value for S, and the angle value for T is also the angle value for R.
So to recap, we will get the equation:
2(3x + 5) + 2(9x - 17) = 360
And solve for x to get your answer.
I hope that made sense and helped a little. :) And you got this!! Geometry is just fancy logic.
