Answer: ![\angle ACB=110^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20ACB%3D110%5E%7B%5Ccirc%7D)
Step-by-step explanation:
Here, The perpendicular bisectors of sides AC and BC of ΔABC intersect side AB at points P and Q respectively, and intersect each other in the exterior (outside) of ![\triangle ABC](https://tex.z-dn.net/?f=%5Ctriangle%20ABC)
Let L is the mid point of side BC while M is the mid point of side AC.(mentioned on below figure).
Then, In triangles QBL and QLC,
QL=QL, ( reflexive)
BL=LC, ( by the property of mid points)
And,
( right angles)
Therefore
, (SAS)
Thus,
( by CPCT)
But, ![\angle LQB+\angle LQC+\angle CQP = 180^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20LQB%2B%5Cangle%20LQC%2B%5Cangle%20CQP%20%3D%20180%5E%7B%5Ccirc%7D)
Thus, ![\angle LQB=59^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20LQB%3D59%5E%7B%5Ccirc%7D)
Now, In
,
![\angle QBL+\angle BLQ+\angle LQB=180^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20QBL%2B%5Cangle%20BLQ%2B%5Cangle%20LQB%3D180%5E%7B%5Ccirc%7D)
⇒
=![\angle ABC](https://tex.z-dn.net/?f=%5Cangle%20ABC)
Similarly, ![\triangle PMC\cong \triangle PMA](https://tex.z-dn.net/?f=%5Ctriangle%20PMC%5Ccong%20%5Ctriangle%20PMA)
Then
( by CPCT)
But, ![\angle CPQ+\angle MPC+\angle MPA = 180^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20CPQ%2B%5Cangle%20MPC%2B%5Cangle%20MPA%20%3D%20180%5E%7B%5Ccirc%7D)
Thus, ![\angle MPA=51^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20MPA%3D51%5E%7B%5Ccirc%7D)
Now, In
,
![\angle MPA+\angle PAM+\angle AMP=180^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20MPA%2B%5Cangle%20PAM%2B%5Cangle%20AMP%3D180%5E%7B%5Ccirc%7D)
⇒
=![\angle BAC](https://tex.z-dn.net/?f=%5Cangle%20BAC)
Again, In
,
![\angle ABC+ \angle BAC+\angle ACB = 180^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20ABC%2B%20%5Cangle%20BAC%2B%5Cangle%20ACB%20%3D%20180%5E%7B%5Ccirc%7D)
![31^{\circ}+39^{\circ}+\angle ACB = 180^{\circ}](https://tex.z-dn.net/?f=31%5E%7B%5Ccirc%7D%2B39%5E%7B%5Ccirc%7D%2B%5Cangle%20ACB%20%3D%20180%5E%7B%5Ccirc%7D)
⇒![\angle ACB=110^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20ACB%3D110%5E%7B%5Ccirc%7D)
4)1,-1
5) 2,1
6)2,1
7) 3,10
8)-3,8
Answer:
When -3v = -18 is solved, the result is:
21v
Answer:
hey, hope the picture helps :)
Answer:
10.3 km
Step-by-step explanation:
Perimeter = side1 + side2 + side3
side1 = 2.7 km
side2 = 3.3 km
side3 = 4.3 km
Perimeter = 2.7 + 3.3 + 4.3
Perimeter = 10.3 km