In circle A shown, BC || DE , mBC=58° and mDE=142°. Determine the measure of ZCFE . Show how you arrived at your answer.
1 answer:
Answer:
< CFE = 40°
Step-by-step explanation:
To better understand the solution, see attachment for the diagram.
Given:
BC parallel to DE
Measure of Arc BD = 58°
Measure of Arc DE = 142°
First step: Draw a diameter that passes through the centre of the circle and name it. In this case, the diameter is line ST.
The line ST divides the arc BD and arc DE into half.
That is:
Arc SC = 1/2(arc BC) =1/2(58)
Arc SC = 29°
Arc TE = 1/2(arc DE) =1/2(142)
Arc TE = 71°
Arc SC + Arc CE + Arc TE = 180° (Sum of angles in a semicircle
29° + Arc CE + 71° = 180°
Arc CE + 100° = 180°
Arc CE = 180-100
Arc CE = 80°
Inscribed angle = 1/2(intercepted angle)
<CFE = 1/2(Arc CE )
<CFE = 1/2(80)
< CFE = 40°
You might be interested in
Answer: Second option, third option and fifth option.
Step-by-step explanation:
In order to solve this exercise it is important to remember the multiplication of signs:
Knowing that, you can distribute the sign and add the like terms. Repeat this procedure in each expression given in the exercise.
Therefore, you get:
You can identify that the expressions ,
and
are equivalent after simplifying.