Drag and drop an answer to each box to correctly complete the proof.

given: m∥nm∥n , m∠1=50∘m∠1=50∘ , and m∠2=42∘m∠2=42∘ .

prove: m∠5=92∘
it is given that m∥nm∥n , m∠1=50∘m∠1=50∘ , and m∠2=42∘m∠2=42∘ . by the , m∠3=88∘m∠3=88∘ . because angles formed by two parallel lines and a transversal are congruent, ∠3≅∠4∠3≅∠4 . by the angle congruence theorem, m∠3=m∠4m∠3=m∠4 . using substitution, 88∘=m∠488∘=m∠4 . angles 4 and 5 form a linear pair, so by the , m∠4+m∠5=180∘m∠4+m∠5=180∘ . substituting gives 88∘+m∠5=180∘88∘+m∠5=180∘ . finally, by the , m∠5=92∘m∠5=92∘ .

Atechnician compares repair costs for two types of microwave ovens (type i and type ii). he believes that the repair cost for type i ovens is greater than the repair cost for type ii ovens. a sample of 6767 type i ovens has a mean repair cost of $79.79$⁢79.79. the population standard deviation for the repair of type i ovens is known to be $19.18$⁢19.18. a sample of 5555 type ii ovens has a mean repair cost of $75.24$⁢75.24. the population standard deviation for the repair of type ii ovens is known to be $21.40$⁢21.40. conduct a hypothesis test of the technician's claim at the 0.050.05 level of significance. let μ1μ1 be the true mean repair cost for type i ovens and μ2μ2 be the true mean repair cost for type ii ovens. step 2 of 4 : compute the value of the test statistic. round your answer to two decimal places.