<h2>
Answer and Explanation to questions 13,14,15</h2>
13)
as given in the question.
14)
Since Y is the midpoint of XZ. So, Y will divide XZ in equal halves into XY and YZ.
15) 
and
. So, 
<h2>
Answer and Explanation to questions 16,17,18</h2>
∠3 is supplementary to ∠1 means: ∠3 + ∠1 = 180°
And, according to figure ∠1 + ∠2 = 180° as ∠1 and ∠2 form a straight line.
∠3 + ∠1 = 180° .............(i)
∠1 + ∠2 = 180° .............(ii)
subtracting equation (i) and (ii) will give ∠3 = ∠2 ..........(iii)
15) ∠3 is supplementary to ∠1 as given in the question
16) ∠2 is supplementary to ∠1 as shown be equation (ii)
18) ∠3 ≅ ∠2 as shown by equation (iii)
<h2>
Answer and Explanation to questions 19</h2>
∠3 and ∠4 form a straight line. Therefore, ∠3 + ∠4 = 180° .......(i)
∠4 and ∠5 form a straight line. Therefore, ∠4 + ∠5 = 180° .......(ii)
subtracting equation (i) and (ii)
∠3 + ∠4 - (∠4 + ∠5) = 180°-(180°)
∠3 + ∠4 - ∠4 - ∠5 = 180°-180°
∠3 - ∠5 = 0
∴ ∠3 = ∠5 (Hence Proved)
(4/5)*what = (2/3)
Multiply by 5/4
.. what = (2/3)*(5/4)
.. what = 5/6
Answer:
<em>24 children</em>
Step-by-step explanation:
If the length of time, y hours, it takes to put a jigsaw puzzle together is inversely proportional to the number of children, x, this is represented as;

k is the constant of proportionality
If it takes 16 children 6 hours to put the jigsaw puzzle together, this means at x = 16, y = 6
Substitute:
6 = k/16
k = 6*16
k = 96
W are to find number of children needed to put the same jigsaw puzzle together in 4 hours, this is done by substituting k = 96 and y = 4 into the expression y = k/x
y = 96/4
y = 24
<em>Hence it will take 24 children to put the same jigsaw puzzle together in 4 hours</em>
<em></em>
X=number of adults, y= number of students
x+y=12
18x+12y=162
You can simplify the second equation by dividing by six: 3x+2y=27
Rearrange the first equation: y= 12-x. Plug y into the simplified second equation:
3x+2(12-x)=27
3x-2x+24=27
x=3.
Plug the now known x value into y=12-x. So y= 9.
Therefore, there are 3 adults and 9 students.