Answer:
11. 5
12. 4
13. 30
14. 3
15. 18
Explanation:
11. You can see that SR and EU are both diagonals so the property of the rectangle is also that the diagonals are equal.
Hence, SR=EU.
So constructing an equation you get 4v+2=6v-8
Rearrange the like terms:
4v-6v=-8-2
-2v=-10
Cancel the subtraction symbol and divide 10 by 2
2v=10
v= 10/2= 5
12. You can see that EC and CU are both joining in the middle of the diagonal which means that both of them are equal and one of them is half of the diagonal.
You can say that EC=CU as mentioned earlier.
So, 2w+3 = 3w-1
Collect the like terms:
2w-3w = -1-3
-1w=-4
w=4 (c1ancelling the subtraction sign)
13. Now, there is a property of a rectangle that says all the angle of the sides is equal to 90
So this means that m∠1+m∠2= 90
x+2x=90
3x=90
x=90/3= 30
14. There is another property of a rectangle that says that the opposite sides are equal which means that UR=SE
So we can form an equation 6y-7 = 4y-1
Collect the like terms:
6y-4y = -1+7
2y = 6
y= 6/2= 3
15. Now look here, the diagonal SR is a straight line, right? So, the sum of m∠4 and m∠3 should be 180 because both of them lie on a straight plain separated by a line. Straight angles are equal to 180.
So, we can form an equation 2z+8z= 180
10z= 180
z= 180/10= 18
I hope everything is crystal clear to you and if any questions feel free to ask me in the comments. Take care :)