Question

42 points! Plus a crown if you are right!! PLEASEE HELPP D:

Answer 1

x = 9

Explanation:

The sum of all the interior angles of a triangle = 180 degrees

one of the angles of the triangle's interior is blank, so to find it we can subtract the exterior angle measure next to it from 180 degrees (a straight line)

38 + (6x + 56) + (180 - (10x + 58)) = 180

Now, we can do our best to simplify and combine like terms:

[38 + 56 + (180 - 58)] + [6x - 10x] = 180

216 - 4x = 180

Now we can subtract 180 from both sides...

36 - 4x = 0

And then add 4x to both sides...

36 = 4x

Now we've manged to isolate x, all that's left is to divide both sides by 4

9 = x

Or

x = 9

Hope this explanation helped! Feel free to ask questions if anything didn't fully make sense!

Answer 2

x = 9

Explanation:

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

Here the exterior angles has a measure of 10x + 58° while its opposite interior angles have measures of 6x + 56° and 38°

If an exterior angle of a triangle is equal to the sum of the opposite interior angles then 10x + 58 = 6x + 56 + 38

we now solve for x

10x + 58 = 6x + 56 + 38

==> combine like terms

10x + 58 = 6x + 94

==> subtract 58 from both sides

10x = 6x + 36

==> subtract 6x from both sides

4x = 36

==> divide both sides by 4

x = 9

and we are done! :)