Problem 5
<h3>Answer: Angle EGF and angle FGB</h3>Explanation:
The straight line EGB can be decomposed into the angle pieces of angle EGF and angle FGB. Another way we can break this straight angle down is to break it into angle EGA and angle AGB. Whichever route you go for, the smaller angles add back to 180 degrees. There are other possible answers you could go for. Check out the diagram below for a visual of these angles (shown in red)
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Problem 6
Answer: Angle AGB and angle EGD
Explanation:
Focus on lines AD and EB. They intersect at point G. The two lines form the opposite angles AGD and EGD which are considered vertical angles. Whenever we have an X shape like this, we'll have vertical angles in the opposite positions like this. Vertical angles are always congruent. There are other pairs of vertical angles shown in this diagram. Check out the diagram below for a visual of these angles (shown in blue)
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Problem 7
<h3>Answer: Angle BGC and Angle CGD</h3>Explanation:
The angles BGC and CGD are right next to each other, so we consider them adjacent. They share the common ray GC. Think of it like two neighbors sharing a common wall in an apartment building. There are other possible answers you could go with as long as the two angles share a common ray or line, and also share a common vertex as well. Check out the diagram below for a visual of these angles (shown in green)
Answer:
Step-by-step explanation:
Area of the sector :
Finding the area given r = 30 ft. and θ = 60° :
⇒ Area = π × (30)² × 60/360
⇒ Area = π × 900/6
⇒ Area = 150π ft²
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Length of the arc :
Finding the arc length given r = 30 ft. and θ = 60° :
⇒ Arc Length = 2 × π × 30 × 60/360
⇒ Arc Length = 60/6 × π
⇒ Arc Length = 10π ft.