The measure of angle H is [tex]28^{\circ}[/tex]
To solve this, create an equation from the statements given as follows:
Let m<H = x
Therefore,
m<G = 2x + 6
Given that, m<G and m<H are complementary angles, it implies that:
m<G + m<H = 90° (sum of complementary angles gives us 90 degrees)
Therefore:
[tex](2x + 6) + x = 90[/tex]
Solve for x
[tex]2x + 6 + x = 90[/tex]
Add like terms
[tex]3x + 6 = 90[/tex]
Subtract 6 from both sides
[tex]3x + 6 - 6 = 90 - 6\\3x = 84[/tex]
Divide both sides by 3
[tex]x = 28[/tex]
Therefore, [tex]m \angle H = x = 28^{\circ}[/tex]
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