Use the given information to find the value of x. use 3.14 for t. c=56.52 feet

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Use the given information to find the value of x. use 3.14 for t. c=56.52 feet

(3x+8)=(5x-20). The angles are vertical so it's equal. You then used the solved for x to solve (3x+8)+(5x+4y)=180 to solve for y. This is because these two angles are supplementary so they add to 180. We assume x is already known from the first equation.

Solving the first equation:

2x=28

x=14

Second equation: 3*14+8+5*14+4y=180

42+8+70+4y=180

4y=180-120

4y=60

y=15

Yes! There is enough information to solve for x. x equals 23 degrees because we know that one angle measure is 23, and that this is a right triangle so another angle measure must be 90. Since we know 2 of the angle measures, we can find the third by subtracting from 180. Seeing as the mid-line bisects this angle and creates a shared side for the 2 triangles, we know the triangles must be congruent. We could also explain this using SAA if needed. To put it short, though, there are several ways we can prove that x=23.

Solution:

1)

Statement Reason

x ║t Given

m∠16=m∠7 Given

m∠16=m∠1 Corresponding angles

m∠7=m∠1 Substitution

k║w Alternate exterior angles equal

(Property of parallel lines)

2)Part A:

Sum of angles in any triangle is 180 degrees.

m∠BAC+m∠ABC+m∠BCA= 180

Substituting the values :

4x+10+12x-6+3x+5=180

Adding like terms :

19x+9=180

19x=171

x=9.

Part B:

Substituting x value :

m∠BAC=4x+10=4(9)+10=46

m∠ABC=12x-6=12(9)-6=102

m∠BCA=3x+5=3(9)+5=32.

Part C:

m∠1=180-46=134

m∠2=180-102=78.

m∠3=180-32=148.

Part D:

Angle BAC and angle FAC are angle made on straight line and are linear .Such angles are called linear pairs.

Part E:

Angle BCE and Angle DCA are vertically opposite angles.

.

∠1 = ∠3 [vertical angles]

5x - 20 = 3x + 8

5x - 3x = 8 + 20

2x = 28

x = 14

m∠1 = 3x + 8 = 3*14 + 8 = 50°

m∠3 = m∠1 = 50°

∠1 + ∠2 = 180° [supplementary angles]

m∠2 = 180 - m∠1 = 180 - 50 = 130°

m∠4 = m∠2 = 130° [vertical angles]

(5x + 4y) = 130 [x = 14]

5*14 + 4y = 130

70 + 4y = 130

4y = 130 - 70

4y = 60

y = 60/4

y = 15

x = 14

y = 15

m∠1= 50°

m∠2= 130°

m∠3= 50°

m∠4= 130°

Because g is the centroid of the triangle abc, then ag = bg= cg

here cg = 3x+7 and bg= 6x

3x+7 = 6x

7=6x-3x

7=3x

x=7/3

for the question to be "workable", af is probably the median, with f on bc

remember the centroid cuts the median in the ratio of 2: 1, or ag: gf = 2: 1

then fg: af= 1: 3

(x+8)/(9x-6) = 1/3

9x - 6 = 3x + 24

6x = 30

x = 5