What is the answer to 16-2t=5t+9
2 answers:
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A diagram of parallelogram MNOP is attached below
We have side MN || side OP and side MP || NO
Using the rule of angles in parallel lines, ∠M and ∠P are supplementary as well as ∠M and ∠N.
Since ∠M+∠P = 180° and ∠M+∠N=180°, we can conclude that ∠P and ∠N are of equal size.
∠N and ∠O are supplementary by the rules of angles in parallel lines
∠O and ∠P are supplementary by the rules of angles in parallel lines
∠N+∠O=180° and ∠O+∠P=180°
∠N and ∠P are of equal size
we deduce further that ∠M and ∠O are of equal size
Hence, the correct statement to complete the proof is
<span>∠M ≅ ∠O; ∠N ≅ ∠P
</span>
We have side MN || side OP and side MP || NO
Using the rule of angles in parallel lines, ∠M and ∠P are supplementary as well as ∠M and ∠N.
Since ∠M+∠P = 180° and ∠M+∠N=180°, we can conclude that ∠P and ∠N are of equal size.
∠N and ∠O are supplementary by the rules of angles in parallel lines
∠O and ∠P are supplementary by the rules of angles in parallel lines
∠N+∠O=180° and ∠O+∠P=180°
∠N and ∠P are of equal size
we deduce further that ∠M and ∠O are of equal size
Hence, the correct statement to complete the proof is
<span>∠M ≅ ∠O; ∠N ≅ ∠P
</span>
Answer:
angle CAB = 113.8 degree
angle ABC = 35.6 degree
angle BCA = 30.6 degree
Step-by-step explanation:
Given data:
A(1, 0, −1),
B(5, −3, 0),
C(1, 5, 2)
calculate the length of side by using the distance formula
so
AB = (5,-3,0) - (1,0,-1) = (4,-3,1)
AC= (1,5,2) - (1,0,-1) = (0,5,3)
|AB|
|AC| =
From following formula, calculate the angle between the two side i.e Ab and AC
AB.AC = |AB|*|AC| cos ∠CAB
(4,-3,1).(0,5,3)
4*0 -3*5 +1*3
-12 =
cos ∠CAB = - 0.404
angle CAB = 113.8 degree
BA =B- A = (1,0,-1) - (5,-3,0) = (-4,3,-1)
BC = (1,5,2)-(5,-3,0) = (-4,8,2)
|BA| = \sqrt{(26)}
|BC|
BA.BC = |BA|*|BC|* cosABC
(-4,3,-1).(-4,8,2) =
16+24-2
cos ∠ABC = 0.813
angle ABC = 35.6 degree
we know sum of three angle in a traingle is 180 degree hence
sum of all three angle = 180
angle BCA + 35.6 + 113.8 = 180
angle BCA = 30.6 degree