Question

1. what values of a and b make △wxy ≅ △fge?

a =
b =

Explanation:

Step1: Set up equations based on congruent triangles

Since \(\triangle WXY\cong\triangle FGE\), corresponding sides are equal. So, \(WY = FE\) and \(XY=GE\).
For \(WY = FE\): \(a + 6b-40=5a + b\).
For \(XY = GE\): \(6a=a + 50\).

Step2: Solve for \(a\) from \(6a=a + 50\)

Subtract \(a\) from both sides: \(6a-a=a + 50-a\).
\(5a=50\).
Divide both sides by \(5\): \(a=\frac{50}{5}=10\).

Step3: Substitute \(a = 10\) into \(a + 6b-40=5a + b\)

Substitute \(a = 10\): \(10+6b-40=5\times10 + b\).
Simplify: \(6b-30 = 50 + b\).
Subtract \(b\) from both sides: \(6b-b-30=50 + b-b\).
\(5b-30=50\).
Add \(30\) to both sides: \(5b-30 + 30=50+30\).
\(5b=80\).
Divide both sides by \(5\): \(b=\frac{80}{5}=16\).

Answer:

\(a = 10\), \(b = 16\)