Question

10. AABC = GEFG. Solve the following problems below: (2 points)

Answer 1

Step 1:

In this question, we are given the following:

Step 2:

The details of the solution are as follows:

a) Solving the value of x, and then find the measure of Angle A:

`\begin{gathered} Triangle\text{ ABC is equaivalent to Triangle EFG} \\ \text{This means that:} \\ Angle\text{ A = Angle E} \\ (3x+20)^0=(5x-80)^0 \\ 3x+20\text{ = 5 x - 80} \\ \text{collecting like terms , we have that:} \\ 20\text{ + 80 = 5x - 3x} \\ 2x\text{ = 100} \\ \text{Divide both sides by 2, we have that:} \\ x\text{ =}(100)/(2) \\ \text{ x = 50} \end{gathered}`
`\begin{gathered} \sin ce\text{ x = 50, we then put x = 50 in the measure of A= 3x+20} \\ A=\text{ ( 3(50) + 20 )} \\ A=\text{ 150 + 20} \\ A=170^0 \end{gathered}`

b) Solving the value of y, and then find the measure of FE and AB:

`\begin{gathered} We\text{ can s}ee\text{ that AB = FE} \\ \\ y+7\text{ =3y-7} \\ \text{collect like terms, we have that:} \\ 7+7=\text{ 3y -y} \\ 2y\text{ = 14} \\ \text{Divide both sides by 2, we have that:} \\ y\text{ = }(14)/(2) \\ y\text{ = 7} \end{gathered}`
`\begin{gathered} \text{Measure of AB : y + 7} \\ \text{where y = 7 , we have that:} \\ 7\text{ + 7 = 14} \\ \text{Measur}e\text{ of AB = 14} \end{gathered}`
`\begin{gathered} \text{Measure of FE: 3y - 7} \\ \text{where y = 7, we have that:} \\ 3(7)\text{ - 7 = 21 - 7 = 14} \\ \text{Measure of FE = 14} \end{gathered}`