Me!
given: ∠1 and ∠2 are supplementary, and ∠2 and ∠3 are supplementary.
prove: ∠1 ≅ ∠3
by definition of supplementary angles, m∠1 + m∠2 = (a) and m∠2 + m∠3 = (b).
then, m∠1 + m∠2 = m∠2 + m∠3 by the (c). subtract m∠2 from each side. you
get m∠1 = (d), or ∠1 ≅ (e).

Step-by-step explanation:

Statement                                                               Reason

1.∠1 and ∠2 are supplementary angles     ---           Given  

2. m∠1 + m∠2 = 180°     ---                  Linear pair, they are supplementary                                

3. m∠1  and m∠3 are supplementary angles --  m∠1 + m∠3= 180

                                                                             (Supplementary angles add upto 180 degrees)  

4.  m∠1 and m∠3                                           Exterior sides in opposite rays

5.   m∠1 + m∠2 = m∠1 + m∠3                         Transitive property  

6.    m∠2 = m∠3                                    Subtraction  property

7.   l || m   If two lines are cut by transversal the alternative interior

so the angles will be supplementary

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950

answer: x=60