The question angle 1 is the supplement of angle 2 while angle 2 & angle 3 are vertical angles measurement of angle 1=n+15 angle 2 =9p and angle 3 is =4n+p find n,p and the measurement of the 3 angles pls help pls show solution or a web site that can help pls .....
antidisestablishmentarianist
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/_1 and /_2 are supplements.. which means that
/_1 + /_2 = 180
=> (n+15) + (9p) = 180
=> n + 9p = 165 ----------- (i)
since /_2 and /_3 are vertical angles, their measures are equal..
so..
/_2 = /_3
=> 9p = 4n + p
=> 8p = 4n
=> n = 2p
put this value of n in equation (i), to get
2p + 9p = 165
=> 11p = 165
=> p = 165/11
=> p = 15
and n = 2p = 30
now you know n and p, and can find the 3 angles using the relations
detektibgapo
Angle 1 = n + 15
Angle 2 = 9p
Angle 3 = 4n + p
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Angle 1 is the supplement of Angle 2 ===> they are supplementary angles.
The sum of the measures of supplementary angles is 180 degrees. Therefore,
( n + 15) + 9p = 180 ===>
n + 15 + 9p = 180 (Equation 1
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Angle 2 and Angle 3 are vertical angles. Vertical angles have the same measures.
Therefore,
9p = 4n + p Equation 2
9p - p = 4n +p - p
8p = 4n
8p/8 = 4n/8
p = 1/2n Equation 3
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Subtitute Equation 3 to Equation 1
n + 15 + 9p = 180 (Equation 1)
n + 15 + 9( 1/2n) = 180
n + 15 + 9/2n = 180
11/2n = 180 - 15
11/2 n = 165
n = 2/11 (165)
n = 330/11
n = 30 degrees ===> value of n
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Substitute the value of n into Equation 2
9p = 4n + p
9p = 4 (30) + p
9p = 120 + p
9p - p = 120 + p - p
8p = 120
p = 120/8
p = 15 degrees ===> value of p
======================
n = 30 , p = 15
Angle 1 = n + 15 = 30 + 15 = 45 degrees
Angle 2 = 9p = 9(15) = 135 degrees
Angle 3 = 4n + p = 4(30) + 15 = 120 + 15 = 135 degrees
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Supplementary Angles
Angle 1 + Angle 2 = 180
45 + 135 = 180
180 = 180
=====================
Vertical ANgles
Angle 2 = ANgle 3
135 = 135
Dianna H
If angle 2 and angle 3 are vertical, then they are congruent (measures equal each other).
If angle 1 and angle 2 are supplementary, then they add to equal 180 degrees.
Therefore we can create two different equations.
9p = 4n + p (using the two vertical angles)
n + 15 + 9p = 180 (using the supplementary angles)
This is now a system of equations. It appears that substitution is the easiest way to solve. Get n alone in the second equation.
n + 15 + 9p = 180
n = 180 - 15 - 9p
n = 165 - 9p
Now plug in 165 - 9p for n in the first equation.
9p = 4n + p
Becomes
9p = 4(165 - 9p) + p
9p = 660 - 36p + p
9p = 660 - 35p
44p = 660
p = 15
To find n, plug 15 in for p in the equation n = 165 - 9p.
n = 165 - 9(15)
n = 165 - 135
n = 30
To find the measures of the angles plug in the appropriate numbers.
Angle 1 = n + 15 = 30 + 15 = 45
Angle 2 = 9p = 9(15) = 135
Angle 3 = 4n + p = 4(30) + 15 = 120 + 15 = 135
sv
1 is the supplement of angle 2 hence n+15 + 9p = 180
angle 2 & angle 3 are vertical angles hence 9p = 4n + p or n = 2p whence 2p + 15 + 9p = 180 or p = 15 and n = 2(15) = 30
angles are 30+15, 9(15), 4(30) + 15 or 45, 135, 135.
Tigre
A1 = n +15 ,A 2 = 9p, A3 = 4n +p
A1 = 180 - A2,
A2 = A3 = 9p = 4n + p = 8p = 4n = 2p = n
A1 = 180 - A2 = n + 15 = 180 - 9p = 2p + 15 = 180 - 15
= 2p + 9p = 11p = 165 ------> divided both side by 11
p = 15.
n = 2p = 2*15 = 30
A1 = n +15 = 30 +15 = 45
A2 = 9p = 9 *15 = 135
A3 = 4n + p = 4*30 + 15 = 135