Answer:
3 = x, y = 6, <AFB = 131, <DAC = 72, <ACD = 29, <DAB = 101
Step-by-step explanation:
#9-10:
Recall that the side lengths of a parallelogram that are parallel to each other, have the same value.
So,
AB = DC and AD = BC
or
3y-8 = 10 and 13 = 2x + 7
13 = 2x + 7
6 = 2x (subtract 7 both sides)
3 = x (divide 2 both sides)
3y-8 = 10
3y = 18 (add 8 both sides)
y = 6 (divide 3 both sides)
#11:
Recall that the angle of a straight line is 180 degrees. This means that <AFC = 180 (although line AC is a diagonal line, the line doesn't have a bend or curve)
If <AFC is split by line BD then,
<AFC = <AFB + <CFB
180 = <AFB + 49
131 (degrees) = <AFB
#12:
Recall that the degree sum of any triangle is 180 degrees.
This means that <AFD + <ADF + <DAF = 180
or,
<AFD + 59 + <DAC = 180
(point F and C are on the same line AC so, <DAF = <DAC)
We can't solve for <DAC until we find <AFD!
Well, <AFD is across <BFC...
Recall vertical angles. They are the angles produced from the cross section of two lines and are oppositely located.
This means that <AFD = <BFC!
Or,
<AFD = 49
Now we can solve the equation!
49 + 59 + <DAC = 180
108 + <DAC = 180 (combine 49 and 59)
<DAC = 72 (subtract 108 both sides)
#13:
Let's focus on triangle DFC.
Using the same fact about the angle sum we have,
<ACD + <DFC + <FDC = 180
We first need to find <DFC and <FDC.
Well, <AFB and <DFC are vertical angles so <DFC = 131.
For <FDC let's recall alternate interior angles. When two parallel lines are cut by a transversal (diagonal line), the pair of angles that are placed opposite from each other (i.e. upper right and lower left) in the space between the two lines are equal to each other.
We know that AB is parallel to DC and we can treat the diagonal line DB as a transversal. So we can say that <ABD = <BDC or 20 = <BDC = <FDC.
Now we can solve for <ACD!
<ACD + 131 + 20 = 180
<ACD + 151 = 180 (combine 131 and 20)
<ACD = 29 (subtract 151 both sides)
#14:
<DAB is the combined angle of <DAC and <FAB (or, <CAB). We know that <DAC = 72, all we need to do is find <FAB!
Recalling alternate interior angles for a second time, we can see that <FAB = <ACD = 29
so,
<ACD + <DAC = <DAB
29 + 72 = 101 = <DAB
Phew! That was a lot so, let me know if you have any questions!