Answer:
a = 35°
b = 14
c = 5
Step-by-step explanation:
A translation maps the blue triangle to the red triangle. So, the red triangle would be the same as the blue triangle. It is just shifted right-left and up-down.
We know the sum of 3 angles in a triangle is 180 degrees. So, we can say:
[tex]55+90+a=180[/tex]
We can interchange all the side and angle values in both blue and red triangle.
Now, we solve for a:
[tex]55+90+a=180\\145+a=180\\a=180-145\\a=35[/tex]
Now,
the left side of blue triangle is same as left side of red triangle, so we can say:
[tex]b+6=20[/tex]
Now we solve for b:
[tex]b+6=20\\b=20-6\\b=14[/tex]
Then,
The bottom of both the triangles are same, so we can say:
[tex]4c-6=14[/tex]
We solve for c:
[tex]4c-6=14\\4c=14+6\\4c=20\\c=5[/tex]
