Unit 7, Lesson 12
Arcs and Sectors
Integrated Math 2
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A circle of radius 12 units is divided into 8 congruent slices.
The image shows a triangle.
Triangle \(ABC\) is shown with its inscribed circle drawn. The measure of angle \(ECF\) is 72 degrees. What is the measure of angle \(EGF\)? Explain or show your reasoning.
How do the values of \(x\) and \(y\) compare? Explain your reasoning.
\(\overline{DF} \perp \overline{FA}\); \(\overline{DE} \perp \overline{EA}\); \(\angle EAD \cong \angle FAD\)Quadrilateral A E D F with line A D bisecting angle A into two 35 degree angles and creating 2 triangles, A D E and A D F. Angle E and F are right angles. D F is x units, D E is y units.
Points \(A,B,\) and \(C\) are the corners of a triangular park. The park district is going to add a set of swings inside the park. The goal is to have the swings equidistant from the vertices of the park. Find a location that meets this goal. Explain or show your reasoning.
In the diagram, the measure of the arc from \(A\) to \(B\) not passing through \(C\) is 80 degrees. What is the measure of angle \(ACB\)?
20 degrees
40 degrees
80 degrees
160 degrees