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Georgia [21]
3 years ago
5

Vertical angles are congruent is that an example of a theorem

Mathematics
2 answers:
NISA [10]3 years ago
7 0
Whats the answers? I need them first


Pachacha [2.7K]3 years ago
3 0

Proof:

<span><span>∠1and∠2</span><span>∠1and∠2</span></span> form a linear pair, so by the Supplement Postulate, they are supplementary. That is,

<span><span>m∠1+m∠2=180°</span><span>m∠1+m∠2=180°</span></span>.

<span><span>∠2and∠3</span><span>∠2and∠3</span></span> form a linear pair also, so

<span><span>m∠2+m∠3=180°</span><span>m∠2+m∠3=180°</span></span>.

Subtracting <span><span>m∠2</span><span>m∠2</span></span> from both sides of both equations, we get

<span><span>m∠1=180°−m∠2=m∠3</span><span>m∠1=180°−m∠2=m∠3</span></span>.

Therefore,

<span><span>∠1≅∠3</span><span>∠1≅∠3</span></span>.

You can use a similar argument to prove that <span><span>∠2≅∠4</span><span>∠2≅∠4</span></span>.In the figure, 

<span><span>∠1≅∠3</span><span>∠1≅∠3</span></span> and <span><span>∠2≅∠4</span><span>∠2≅∠4</span></span>.

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Please add explanation
Igoryamba

The answer is C

The equation has x = 8/10

To get X by itself you need to divide both sides by 8, so the equation should become X = 10/8

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3 years ago
The sum of three numbers is 8. The third is 9
Ierofanga [76]

Answer:

→<u> </u><u>First</u><u> </u><u>value</u><u> </u><u>is</u><u> </u><u>1</u>

→<u> </u><u>Second</u><u> </u><u>value</u><u> </u><u>is</u><u> </u><u>2</u>

→<u> </u><u>Third</u><u> </u><u>value</u><u> </u><u>is</u><u> </u><u>5</u>

Step-by-step explanation:

• let numbers be x, y and z

{ \tt{z = 8y - 9 -  -  - (eqn \: 1)}} \\  \\ { \tt{10x = 8y - 7 -  -  - (eqn \: 2)}} \\  \\ { \tt{x + y + z = 8 -  -  - (eqn \: 3)}}

• from eqn 2, make x the subject:

{ \tt{x =  \frac{8y - 7}{10} }} \\

• substitute all variables in eqn 3:

{ \tt{ \frac{8y - 7}{10}  + y + 8y - 9 = 8}} \\  \\ { \tt{8y - 7 + 10y + 80y - 90 = 80}} \\  \\ { \tt{98y = 177}} \\  \\ { \boxed{ \tt{ \: y = 1.8}}}

• find z

{ \tt{z = 8y - 9}} \\  \\ { \tt{z = 8(1.8) - 9}} \\  \\ { \tt{z = 14.4 - 9}} \\  \\ { \boxed{ \tt{ \: z = 5.4 \: }}}

• find x:

{ \tt{x =  \frac{8(1.8) - 7}{10} }} \\  \\ { \tt{x =  \frac{7.4}{10} }} \\  \\ { \boxed{ \tt{ \: x = 0.74 \: }}}

Rounding to nearest value:

{ \boxed{ \rm{x = 1}}} \\ { \boxed{ \rm{y =2 }}} \\ { \boxed{  \rm{z = 5}}}

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Answer:

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Isolate the variables by dividing each side by -2.5.

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