Trying to help my Autistic child with geometry. Need a simple step by step explanation and answer please. In this open ended question, find each item and include an explanation of how you found each one. Find arc AD. Find angle APD. If arc BC=100 degrees, find angle EBC. Find arc AB. Find the area of sector APD.
Information off the diagram is: ABD has a 65 degree angle. DBC has a 30 degree angle. The radius of the circle is 3.
To find each item in the given open-ended question, we will break it down step by step and explain how to find each one.
1. Find arc AD:
First, we need to understand that the measure of an arc is equal to the measure of its corresponding angle at the center of the circle. Since we know that angle ABD is 65 degrees, we can say that arc AD is also 65 degrees.
2. Find angle APD:
Angle APD is an inscribed angle that intercepts arc AD. According to the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of its intercepted arc. Since arc AD is 65 degrees, angle APD is half of that, which is 32.5 degrees.
3. If arc BC = 100 degrees, find angle EBC:
To find angle EBC, we can apply the same concept as before. Angle EBC is the central angle that intercepts arc BC. Since arc BC is 100 degrees, angle EBC will also be 100 degrees.
4. Find arc AB:
Since arc AB is the remaining part of the circle that is not mentioned in the given information, we can find it by subtracting the measures of arcs AD and BC from the total measure of a circle, which is 360 degrees. Therefore, arc AB = 360° - (arc AD + arc BC) = 360° - (65° + 100°) = 360° - 165° = 195°.
5. Find the area of sector APD:
The formula to find the area of a sector is A = (θ/360°) * π * r², where θ is the angle of the sector in degrees and r is the radius of the circle. In this case, angle APD is 32.5 degrees and the radius is given as 3. Plugging in these values, we get A = (32.5/360°) * π * 3² = (0.09) * 3.14 * 9 = 0.2546 * 9.42 ≈ 2.396 square units.
By following these step-by-step explanations, the answers to each part of the open-ended question are as follows:
- arc AD = 65 degrees
- angle APD = 32.5 degrees
- angle EBC = 100 degrees
- arc AB = 195 degrees
- area of sector APD ≈ 2.396 square units.
Where is E ?
Where is P ?
Are your given points A,B,and C on the circle?