Congruent triangles have equal side and angle measures.
The values of x and y 12 and 8
[tex]\mathbf{\triangle MTW \cong \triangle BGK}[/tex] means that
- [tex]\mathbf{\angle M \cong \angle B}[/tex]
- [tex]\mathbf{\angle T \cong \angle G}[/tex]
- [tex]\mathbf{\angle W \cong \angle K}[/tex]
So, we have:
[tex]\mathbf{4x - 3 =45}[/tex]
Add 3 to both sides
[tex]\mathbf{4x =48}[/tex]
Divide both sides by 4
[tex]\mathbf{x =12}[/tex]
Next, we calculate angle M using:
[tex]\mathbf{\angle M + \angle T + 41 = 180}[/tex]
Recall that: [tex]\mathbf{\angle T \cong \angle G}[/tex]
So, we have:
[tex]\mathbf{\angle M + \angle G + 41 = 180}[/tex]
Substitute 45 for G
[tex]\mathbf{\angle M + 45 + 41 = 180}[/tex]
[tex]\mathbf{\angle M + 86 = 180}[/tex]
Subtract 86 from both sides
[tex]\mathbf{\angle M = 94}[/tex]
Recall that [tex]\mathbf{\angle M \cong \angle B}[/tex]
So, we have:
[tex]\mathbf{11y + 6 = 94}[/tex]
Subtract 6 from both sides
[tex]\mathbf{11y = 88}[/tex]
Divide both sides by 11
[tex]\mathbf{y = 8}[/tex]
So, we have:
[tex]\mathbf{x =12}[/tex] and [tex]\mathbf{y = 8}[/tex]
Hence, the values of x and y are 12 and 8, respectively
Read more about congruent triangles at:
https://brainly.com/question/14150585
