If 180°< α< 270°, cos⁡ α=−8/17, 270°< β< 360°, and sin⁡ β=−4/5, what is cos⁡(α+β)?

cos(\alpha+\beta)=-\frac{84}{85}

Step-by-step explanation:

we know that

Remember the identity

step 1

Find the value of  

we have that

The angle alpha lie on the III Quadrant

so

The values of sine and cosine are negative

Find the value of sine

substitute

step 2

Find the value of  

we have that

The angle beta lie on the IV Quadrant

so

The value of the cosine is positive and the value of the sine is negative

Find the value of cosine

substitute

step 3

Find cos⁡ (α + β)

we have

substitute

i think it is everything has to equal 180 so, if i correct 4=c. 6=d. 8=a. 7=b. and the last question would be c. because they are parallel lines and they are congruent.

step-by-step explanation:

the reason everything has to equal to 180 is because that is how it works. i'm guessing that is its rule. 4 and 8 are congruent and parallel so, that would be 30+30 because they have the same number. it would equal 60. 6 and 7 are congruent and parallel so, that would be 30+30 because they have the same number. it would equal 60. 60+60 is 180. so, now you have your answer