If ΔABC is similar to ΔDEF, the m∠A = 50°, and m∠E = 70°, what is m∠C?

Mathematics

2 answers:

siniylev [52]3 years ago

7 0

Answer: A) $60^{\circ}$

Step-by-step explanation:

Given: ΔABC is similar to ΔDEF

Therefore,

∠A=∠D=50°

∠B=∠E=70°

∠C=∠F

Using Angle sum property, in triangle ABC, we get

$\angle{A}+\angle{B}+\angle{C}=180^{\circ}\\\\\Rightarrow\ 50^{\circ}+70^{\circ}+\angle{C}=180^{\circ}\\\\\Rightarrow\ 120^{\circ}\angle{C}+=180^{\circ}\\\\\Rightarrow\ \angle{C}=180^{\circ}-120^{\circ}\\\\\Rightarrow\ \angle{C}=60^{\circ}$

The angle sum property of a triangle says that, the sum of all the angles in a triangle is $180^{\circ}$ .

MAVERICK [17]3 years ago

6 0

Ok so if they are similar that means equal angles so 50+70=120 then 180-120=60 so the answer is A. <span>#TeamAlvaxic</span>

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Plastic parts produced by an injection-molding operation are checked for conformance to specifications. Each tool contains 15 ca

Rainbow [258]

Answer:

(A) 0.006593 or 0.6593%

(B) 0.01538 or 1.538%

Step-by-step explanation:

The total number of possibilities to pick 3 parts out of 15 possible parts is given by the following combination:

$n=\frac{15!}{(15-3)!3!}=\frac{15*14*13}{3*2*1}\\n=455\ ways\\$

(A) There are only three possibilities for which the inspector finds exactly one nonconforming part (NCC, CNC, CCN). Therefore, the probability is:

$P(N=1) = \frac{3}{455}=0.006593 =0.6593\%$

(B) There are three possibilities for which the inspector finds exactly one nonconforming part, three possibilities for two nonconforming parts (NNC, CNN, NCN), and one possibility for all nonconforming parts (NNN). The probability that the inspector finds at least one nonconforming part is:

$P(N>0) =P(N=1)+P(N=2)+P(N=3) \\P(N>0) = \frac{3}{455}+ \frac{3}{455}+ \frac{1}{455}\\P(N>0) =0.01538 =1.538\%$