Identify the theorem or postulate that is related to the measures of the angles in the pair, and find the unknown angle measures. m∠1=(30x−30)∘, m∠5=(40x+70)∘

Alt. Int. ∠s Thm.

m∠1 = 30°, m∠5 = 150°

Alt. Int. ∠s Thm.

m∠1 = 30°, m∠5 = 30°

Same-Side Int. ∠s Thm.

m∠1 = 30°, m∠5 = 150°

Same-Side Int. ∠s Thm.

m∠1 = 150°, m∠5 = 30°

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

answer: first option i.e. 'a' is correct.

step-by-step explanation:

since we have given that

number of minutes to wrap a small gift box = 4 minutes

we need to find the number of gifts to be wrapped in 5 minutes

since there is a direct variation, as the number of minutes will increase with   number of gifts to be wrapped.

so, let the number of gifts to be wrapped in 5 minutes be x.

so, it becomes,

hence, first option 'a'   is correct.