The sum of exterior angles in total: 360 degrees
6th angle = 78+50+89+37+65= 319
Then 360-319= 41 degrees
Answer: B. 1.85 + x = 5.30
Explanation:
The starting height of the tree was 1.85 meters. To find the number of meters the tree grew, you would subtract the current height from the previous height.
5.30-1.85=x. This equation is the same as 1.85 + x = 5.30 if you switch the 5.30 and x.
The answer is: " 91 " .
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→ " B = 91 " .
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Explanation:
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Given:
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" A + B = 180 " ;
"A = -2x + 115 " ; ↔ A = 115 − 2x ;
"B = - 6x + 169 " ; ↔ B = 169 − 6x ;
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METHOD 1)
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Solve for "x" ; and then plug the solved value for "x" into the expression given for "B" ; to solve for "B"
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(115 − 2x) + (169 − 6x) =
115 − 2x + 169 − 6x = ?
→ Combine the "like terms" ; as follows:
+ 115 + 169 = + 284 ;
− 2x − 6x = − 8x ;
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And rewrite as:
" − 8x + 284 " ;
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→ " - 8x + 284 = 180 " ;
Subtract: "284" from each side of the equation:
→ " - 8x + 284 − 284 = 180 − 284 " ;
to get:
→ " -8x = -104 ;
Divide EACH SIDE of the equation by "-8 " ;
to isolate "x" on one side of the equation; & to solve for "x" ;
→ -8x / -8 = -104/-8 ;
→ x = 13
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Now, to find the value of "B" :
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"B = - 6x + 169 " ; ↔ B = 169 − 6x ;
↔ B = 169 − 6x ;
= 169 − 6(13) ; ===========> Plug in our "solved value, "13", for "x" ;
= 169 − (78) ;
= 91 ;
B = " 91 " .
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The answer is: " 91 " .
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→ " B = 91 " .
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Now; let us check our answer:
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→ A + B = 180 ;
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Plug in our "solved answer" ; which is "91", for "B" ; as follows:
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→ A + 91 = ? 180? ;
↔ A = ? 180 − 91 ? ;
→ A = ? -89 ? Yes!
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→ " A = -2x + 115 " ; ↔ A = 115 − 2x ;
Plug in our solved value for "x"; which is: "13" ;
" A = 115 − 2x " ;
→ A = ? 115 − 2(13) ? ;
→ A = ? 115 − (26) ? ;
→ A = ? 29 ? Yes!
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METHOD 2)
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Given:
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" A + B = 180 " ;
"A = -2x + 115 " ; ↔ A = 115 − 2x ;
"B = - 6x + 169 " ; ↔ B = 169 − 6x ;
→ Solve for the value of "B" :
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A + B = 180 ;
→ B = 180 − A ;
→ B = 180 − (115 − 2x) ;
→ B = 180 − 1(115 − 2x) ; ==========> {Note the "implied value of "1" } ;
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Note the "distributive property" of multiplication:__________________________________________________ a(b + c) = ab + ac ; <u><em>AND</em></u>:
a(b − c) = ab − ac .________________________________________________________
Let us examine the following part of the problem:
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→ " − 1(115 − 2x) " ;
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→ " − 1(115 − 2x) " = (-1 * 115) − (-1 * 2x) ;
= -115 − (-2x) ;
= -115 + 2x ;
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So we can bring down the: " {"B = 180 " ...}" portion ;
→and rewrite:
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→ B = 180 − 115 + 2x ;
→ B = 65 + 2x ;
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Now; given: "B = - 6x + 169 " ; ↔ B = 169 − 6x ;
→ " B = 169 − 6x = 65 + 2x " ;
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→ " 169 − 6x = 65 + 2x "
Subtract "65" from each side of the equation; & Subtract "2x" from each side of the equation:
→ 169 − 6x − 65 − 2x = 65 + 2x − 65 − 2x ;
to get:
→ " - 8x + 104 = 0 " ;
Subtract "104" from each side of the equation:
→ " - 8x + 104 − 104 = 0 − 104 " ;
to get:
→ " - 8x = - 104 ;
Divide each side of the equation by "-8" ;
to isolate "x" on one side of the equation; & to solve for "x" ;
→ -8x / -8 = -104 / -8 ;
to get:
→ x = 13 ;
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Now, let us solve for: " B " ; → {for which this very question/problem asks!} ;
→ B = 65 + 2x ;
Plug in our solved value, " 13 ", for "x" ;
→ B = 65 + 2(13) ;
= 65 + (26) ;
→ B = " 91 " .
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Also, check our answer:
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Given: "B = - 6x + 169 " ; ↔ B = 169 − 6x = 91 ;
When "x = 13 " ; does: " B = 91 " ?
→ Plug in our "solved value" of " 13 " for "x" ;
→ to see if: "B = 91" ; (when "x = 13") ;
→ B = 169 − 6x ;
= 169 − 6(13) ;
= 169 − (78)______________________________________________________
→ B = " 91 " .
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Answer:
10/13
Step-by-step explanation:
if this is wrong, im sorry, but im pretty sure its correct
Answer:
74 degrees
Step-by-step explanation:
The arc degree measurement of the arc that is colored in orange is given as 254 degrees.
The remaining part is the part in green.
The green part plus the orange part should equal 360 degrees because that would make a full rotation around the circle.
.
The green arc has measurement 106 degrees.
We can find x by computing half the difference of the arcs there.
That is,
