Question

Two complementary angles have measures of `s` and `t`. If `t` is 9 less than twice `s`, what are the measures of each angle?​

Answer 1

Answer:

S measures 33° and t measures 57°.

Step-by-step explanation:

Since the two angles s and t are complementary, this implies that:

• $m\angle s+m\angle t=90$

We are given that t is 9 less than twice s. Hence:

• $m\angle t=2m\angle s-9$

We can substitute this into the first equation:

• $m\angle s+(2m\angle s-9)=90$

Solve for s. Combine like terms:

• $3m\angle s-9=90$

Adding 9 to both sides yields:

• $3m\angle s=99$

And dividing both sides by 3

gives us that:

• $m\angle s=33^\circ$

Returning to our second equation, we have:

• $m\angle t=2m\angle s-9$

So:

• $m\angle t=2(33)-9=66-9=57^\circ$

So, ś measures 33° and ť measures 57°.