Question

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Geometry Question:
What is the value of each variable? Please show all work on how you got your answers

Answer 1

a = 35°

b = 14

c = 5

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:

`55+90+a=180`

We can interchange all the side and angle values in both blue and red triangle.

Now, we solve for a:

`55+90+a=180\\145+a=180\\a=180-145\\a=35`

Now,

the left side of blue triangle is same as left side of red triangle, so we can say:

`b+6=20`

Now we solve for b:

`b+6=20\\b=20-6\\b=14`

Then,

The bottom of both the triangles are same, so we can say:

`4c-6=14`

We solve for c:

`4c-6=14\\4c=14+6\\4c=20\\c=5`