Given:
m(ar QT) = 220
m∠P = 54
To find:
The measure of arc RS.
Solution:
PQ and PT are secants intersect outside a circle.
<em>If two secants intersects outside a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.</em>
![$\Rightarrow \angle P = \frac{1}{2} (m \ ar (QT) - m \ ar (RS ))](https://tex.z-dn.net/?f=%24%5CRightarrow%20%5Cangle%20P%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%28m%20%5C%20ar%20%28QT%29%20-%20m%20%5C%20ar%20%28RS%20%29%29)
![$\Rightarrow 54 = \frac{1}{2} (220- m \ ar (RS ))](https://tex.z-dn.net/?f=%24%5CRightarrow%2054%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%28220-%20m%20%5C%20ar%20%28RS%20%29%29)
Multiply by 2 on both sides.
![$\Rightarrow 2 \times 54 = 2 \times \frac{1}{2} (220- m \ ar (RS ))](https://tex.z-dn.net/?f=%24%5CRightarrow%202%20%5Ctimes%2054%20%3D%202%20%5Ctimes%20%20%5Cfrac%7B1%7D%7B2%7D%20%28220-%20m%20%5C%20ar%20%28RS%20%29%29)
![$\Rightarrow 108= 220- m \ ar (RS )](https://tex.z-dn.net/?f=%24%5CRightarrow%20108%3D%20220-%20m%20%5C%20ar%20%28RS%20%29)
Subtract 220 from both sides.
![$\Rightarrow 108-220= 220- m \ ar (RS )-220](https://tex.z-dn.net/?f=%24%5CRightarrow%20108-220%3D%20220-%20m%20%5C%20ar%20%28RS%20%29-220)
![$\Rightarrow -112= -m \ ar (RS )](https://tex.z-dn.net/?f=%24%5CRightarrow%20-112%3D%20-m%20%5C%20ar%20%28RS%20%29)
Multiply by (-1) on both sides.
![$\Rightarrow (-112)\times(-1)= -m \ ar (RS )\times(-1)](https://tex.z-dn.net/?f=%24%5CRightarrow%20%28-112%29%5Ctimes%28-1%29%3D%20-m%20%5C%20ar%20%28RS%20%29%5Ctimes%28-1%29)
![$\Rightarrow 112= m \ ar (RS )](https://tex.z-dn.net/?f=%24%5CRightarrow%20112%3D%20m%20%5C%20ar%20%28RS%20%29)
The measure of arc RS is 112.
Answer:
look down below
Step-by-step explanation:
We know that AB = DC, and BC = AD, ∠B = ∠D because they are given
So, ΔABC ≅ ΔCDA because of SAS congruency
Answer:
160
Step-by-step explanation:
- 8
- 16
- 24
- 32
- 40
- 48
- 56
- 64
- 72
- 80
- 88
- 96
- 104
- 112
- 120
- 128
- 136
- 144
- 152
- 160
Answer:
Volume of solid = 737 cm³ (Approx)
Step-by-step explanation:
Given:
Radius r = 4 cm
Length of cylinder = 12 cm
Find:
Volume of solid
Computation:
Volume of solid = Volume of hemisphere + Volume of cylinder
Volume of solid = (2/3)πr³ + πr²h
Volume of solid = (2/3)π(4)³ + π(4)²(12)
Volume of solid = 134 + 603
Volume of solid = 737 cm³ (Approx)