2x-5y= -5
-2/*x+2y=11
2x-5y= -5
-2x-4y= -22
+------------------
-9y=-27
y=3
x+2y=11
x+2*3=11
x=5
A convex figure with three sides is triangle. The sum of the measures of all interior angles of the triangle is 180°.
Let
be interior angles of this triangle. Then
![\alpha+\beta+\gamma=180^{\circ}.](https://tex.z-dn.net/?f=%5Calpha%2B%5Cbeta%2B%5Cgamma%3D180%5E%7B%5Ccirc%7D.)
Find exterior angles of this triangle:
1.
is exterior angle adjacent to the interior angle ![\alpha.](https://tex.z-dn.net/?f=%5Calpha.)
2.
is exterior angle adjacent to the interior angle ![\beta.](https://tex.z-dn.net/?f=%5Cbeta.)
3.
is exterior angle adjacent to the interior angle ![\gamma.](https://tex.z-dn.net/?f=%5Cgamma.)
The sum of the measures of all exterior angles is
![180^{\circ}-\alpha+180^{\circ}-\beta+180^{\circ}-\gamma=540^{\circ}-(\alpha+\beta+\gamma)=540^{\circ}-180^{\circ}=360^{\circ}.](https://tex.z-dn.net/?f=180%5E%7B%5Ccirc%7D-%5Calpha%2B180%5E%7B%5Ccirc%7D-%5Cbeta%2B180%5E%7B%5Ccirc%7D-%5Cgamma%3D540%5E%7B%5Ccirc%7D-%28%5Calpha%2B%5Cbeta%2B%5Cgamma%29%3D540%5E%7B%5Ccirc%7D-180%5E%7B%5Ccirc%7D%3D360%5E%7B%5Ccirc%7D.)
Answer: 360°
The second choice (18...) is the closest estimate.
Answer:
m<T = 20°
Step-by-step explanation:
m<R = 140°
m<S = 100°
The figure given is a kite. The angles formed where two unequal sides meet are always congruent to each other. This means:
m<S = m<U = 100°
Sum of all interior angles of a quadrilateral = 360°
Therefore:
m<T = 360° - (m<S + m<U + m<R)
m<T = 360° - (100° + 100° + 140°) (substitution)
m<T = 20°