Question

I could use some help on this

Answer 1

when you add 2 Complementary angles they equal 90 degrees.

The ratio is 2:7

2X + 7X = 90

9X = 90

X = 10

Smaller angle = 2X = 2(10) = 20 degrees.

Answer 2

keeping in mind that complementary angles sum up to 90°, let's say we have "a" and "b", and thus a + b = 90°, and they're on a 2:7 ratio.

$\bf \cfrac{a}{b}\qquad 2:7\qquad \cfrac{a}{b}=\cfrac{2}{7}\implies 7a=2b\implies \boxed{a}=\cfrac{2b}{7} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ a+b=90\implies \left( \boxed{\frac{2b}{7}} \right)+b=90\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{7}}{2b+7b=630} \\\\\\ 9b=630\implies b=\cfrac{630}{9}\implies \blacktriangleright b=70 \blacktriangleleft~\hfill \blacktriangleright a=20 \blacktriangleleft$