2.) Find the measure of exterior angle X:

Mathematics

2 answers:

Oxana [17]3 years ago

6 0

ANSWER:
try 110 , sorry if that’s wrong

Maslowich3 years ago

4 0

Answer:

x = 90

Step-by-step explanation:

<u><em>Here 60 is angle B, 30 is Angle a, B is The third angle of the triangle, and x is the exterior angle measurement! </em></u>

60 + 30 + b= 180

a + x = 180

60 + 30 + b= 180

90 + b = 180

b = 90

90 + x = 180

x = 90

exterior angle equal to the sum of its<em> two opposite non-adjacent interior angles.</em>

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e) Given the following: Let X = {1, 2, 3, 4) and a relation R on X as R= {(1,2), (2,3), (3,4)}. Find the reflexive and transitiv

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The answer is $\{(1,1),(2,2),(3,3),(4,4),(1,2)(2,3)(3,4),(1,3),(1,4)\}$

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Remember that a reflexive relation $R\subset \mathcal{P}(X)$ , where $\mathcal{P}(X)$ is the power set of $X$ , is one which conteins the ordered pairs of the form $(a,a)$ , for $a\in X$ .

So, As the reflexive and transitive closure of $R$ (that we will denote by $\overline{R}$ ) is in particular reflexive, we must add to $R$ the elements $\{(1,1) , (2,2),(3,3),(4,4) \}$

A transitive relation $R$ is one in which if the pair $(a,b)$ and the pair $(b,c)$ are in there, then the pair $(a,c)$ must be there too.

So, to complete the relation $R$ to be reflexive and transitive we must add the pair $(1,3)$ (because $(1,2),(2,3)$ are in $R$ ), the pair $(2,4)$ , and the pair $(1,4)$ because we added the pair $(2,4)$ .