The values are t=3 inches and x=12.
The given information states that triangles ABC and KLM are congruent, denoted as ΔABC ≅ ΔKLM. For triangles to be congruent, their corresponding sides and angles must be equal in measure.
From the given information:
BC=9 inches (in)
∠C=36
LK=3t inches (in)
M=3x
In congruent triangles, corresponding sides are proportional, so we can set up the following equalities based on the corresponding sides:
BC=LK
9=3t
Solving this equation for t:
3t=9
t= 9/3
t=3
So, we have found the value of t to be 3 inches.
Additionally, the corresponding angles in congruent triangles are equal, so:
∠C=∠M
36=3x
Solving this equation for x:
3x=36
x= 36/3
x=12
Therefore, the values are t=3 inches and x=12.