Question

For two acute angles ∠E and ∠F, cos(E)=sin(F). Let m∠E=(8x–12)° and m∠F=(6x–10)°. What is m∠F, in degrees?

Answer 1

If cos(E) = sin(F), then we know that m∠E + m∠F = 90 degrees (since E and F are acute angles).

We are given that m∠E = (8x - 12) degrees, and we want to find m∠F.

We can substitute the given value of m∠E into the equation m∠E + m∠F = 90 degrees, and solve for m∠F:

(8x - 12) + m∠F = 90

m∠F = 78 - 8x

So the measure of angle F is 78 - 8x degrees.

We are also given that m∠F = (6x - 10) degrees. So we can substitute this value into the equation we just found:

m∠F = (6x - 10) = 78 - 8x

We can now solve this equation for x:

6x - 10 = 78 - 8x

14x = 88

x = 6

So we know that x = 6.

Now we can substitute this value back into the equation m∠F = (6x - 10) to find the measure of angle F:

m∠F = (6x - 10) = (6 * 6) - 10 = 24 degrees

So the measure of angle F is 24 degrees.