Question

If the triangles are similar, what is the value of x?

Answer 1

x=54

Explanation:

3*16=48 ( less than 90 degrees )

3*38=114

3*42=126

3*54=162

Answer 2

`42\\`

Explanation:

A triangles angles add up to 180°. We know two angle measures in the triangles and, since they are similar, they will have the same measure. You can mirror the measures from one triangle to another. Solve for the unknown angle:

`16+126+a=180`

a represents the unknown angle adjacent to 3x btw

`142+a=180`

`142-142+a=180-142`

`a=38`

the missing angle measure is 38. Now, we can see that there is a straight angle (180°) that unites 16°, 3x°, and the angle that is now known as 38°. So we add the known degrees together

`16+38=54`

Subtract from the total value of 180

`180-54=126`

126 is the obtuse angle measure, so now solve for x

`3x=126`

`(3x)/(3) =(126)/(3) \\\\x=42`