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DIA [1.3K]
3 years ago
8

Given that the measure of angle GHJ = 154 degrees find the angle of HIJ

Mathematics
1 answer:
vichka [17]3 years ago
6 0

Answer:

the correct answer is 77°

Step-by-step explanation:

Angle GHJ and IHJ form supplementary angles which add up to 180°

therefore angle IHJ=180-154

angle IHJ=26°

Triangle IHJ is an isosceles triangle whose base angles HIJand IJH are equal. Lets assign them the same value, x° each

since the sum of all interior angles of a triangle add up to 180°, then x°+x°+26°=180°

2x+26=180

2x=154°

x=77°

Therefore both HIJ and IJH measure 77°

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Klio2033 [76]

Answer:

\{T(v_1), T(v_2), T(v_3)\} is linearly dependent set.

Step-by-step explanation:

Given:  \{v_1,v_2,v_3\} is a linearly dependent set in set of real numbers R

To show: the set \{T(v_1), T(v_2), T(v_3)\} is linearly dependent.

Solution:

If \{v_1,v_2,v_3,...,v_n\} is a set of linearly dependent vectors then there exists atleast one k_i:i=1,2,3,...,n such that k_1v_1+k_2v_2+k_3v_3+...+k_nv_n=0

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A linear transformation T: U→V satisfies the following properties:

1. T(u_1+u_2)=T(u_1)+T(u_2)

2. T(au)=aT(u)

Here, u,u_1,u_2∈ U

As T is a linear transformation,

k_1T(v_1)+k_2T(v_2)+k_3T(v_3)=0\\T(k_1v_1)+T(k_2v_2)+T(k_3v_3)=0\\T(k_1v_1+k_2v_2+k_3v_3)=0\\

As \{v_1,v_2,v_3\} is a linearly dependent set,

k_1v_1+k_2v_2+k_3v_3=0 for some k_i\neq 0:i=1,2,3

So, for some k_i\neq 0:i=1,2,3

k_1T(v_1)+k_2T(v_2)+k_3T(v_3)=0

Therefore, set \{T(v_1), T(v_2), T(v_3)\} is linearly dependent.

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