Step-by-step explanation:
As these two triangles are similar we know a few things:
Their respective angles will have the same measure
Their respective sides will be proportional to each other.
Knowing this, we can sole for x by creating a proportion of the two given sides
[tex]\frac{42}{60} =\frac{x+12}{40}[/tex]
Now we can solve for x
[tex]\frac{42}{60} =\frac{x+12}{40}\\\\\frac{40(42)}{60} =x+12\\x=\frac{1680}{60} -12\\\\x=28-12\\\\x=16[/tex]
Knowing that the respective angles will be equal we can create this equation to solve for y
[tex]5y+7=52\\\\5y=45\\\\y=9[/tex]
And knowing that, again, the angles will be equal to each other If we solve for angle E, we can know the measure of angle H
We are given two of the angles of GEF and the sum of the angles of a triangle is always 180. We can setup an equation as follows
[tex]52+36+E=180\\\\E=92\\E=92=H[/tex]
