Answer:
[tex]80[/tex]° and [tex]10[/tex]°
Step-by-step explanation:
Complementary angles are a pair of angles whose measures have a sum of [tex]90[/tex]°. Therefore, if we let the measure of the bigger angle be [tex]x[/tex], then the measure of the smaller angle will be [tex]x-70[/tex] because we are given that the difference of the measures of the two angles is [tex]70[/tex]°. We can write the following equation to solve for [tex]x[/tex]:
[tex]x+x-70=90[/tex]
Solving for [tex]x[/tex], we get:
[tex]x+x-70=90[/tex]
[tex]2x-70=90[/tex] (Simplify LHS)
[tex]2x-70+70=90+70[/tex] (Add [tex]70[/tex] to both sides of the equation to isolate [tex]x[/tex])
[tex]2x=160[/tex] (Simplify)
[tex]\frac{2x}{2}=\frac{160}{2}[/tex] (Divide both sides of the equation by [tex]2[/tex] to get rid of [tex]x[/tex]'s coefficient)
[tex]x=80[/tex] (Simplify)
Therefore, the measure of one angle is [tex]80[/tex]° and the measure of the other angle is [tex]x-70=80-70=10[/tex]°. Hope this helps!
