Problem 1
Draw a straight line and plot P anywhere on it. Use the compass to trace out a faint circle of radius 8 cm with center P. This circle crosses the previous line at point Q.
Repeat these steps to set up another circle centered at Q and keep the radius the same. The two circles cross at two locations. Let's mark one of those locations point X. From here, we could connect points X, P, Q to form an equilateral triangle. However, we only want the 60 degree angle from it.
With P as the center, draw another circle with radius 7.5 cm. This circle will cross the ray PX at location R.
Refer to the diagram below.
=====================================================
Problem 2
I'm not sure why your teacher wants you to use a compass and straightedge to construct an 80 degree angle. Such a task is not possible. The proof is lengthy but look up the term "constructible angles" and you'll find that only angles of the form 3n are possible to make with compass/straight edge.
In other words, you can only do multiples of 3. Unfortunately 80 is not a multiple of 3. I used GeoGebra to create the image below, as well as problem 1.
Answer: there is only one solution
Step-by-step explanation:
Combine like terms by performing the opposite operation of subtracting 4x on both sides of the equation
The 4x's will cross out on the right
4x - 4x = 0x = 0
On the left:
2x - 4x = -2x
Now the equation looks like:
-2x + 3 = 2
Continue to combine like terms by subtracting 3 on both sides of the equation
On the left:
3 - 3 = 0
On the right:
2 - 3 = -1
Equation:
-2x = -1
Isolate x by performing the opposite operation of dividing -2 on both sides of the equation
On the left:
-2x ÷ -2 = 1
On the right:
-1 ÷ -2 = 1/2
x= 1/2
Sajia can sell 21 books she can sell if she comes back on sunday and the required inequality is 
<em><u>Solution:</u></em>
Given that Sajia has 30 Books in her library
She sold 9 books at the thrift store on Saturday
To find: We have to write and solve an inequality to determine number of more books she can sell if she comes back on sunday
Let "x" be the number of more books she can sell if she comes back on sunday
<em><u>We can write a inequality as:</u></em>
Now moving 9 from L.H.S to R.H.S we get,
On solving 30 - 9 = 21,
So Sajia can sell 21 books she can sell if she comes back on sunday
Answer:
Step-by-step explanation:
the coordinates of midpoint is average of x value of endpoints and average of y value of endpoints
