Margot has started a construction and has this drawn on her paper. What is she constructing?
2 answers:
For a better understanding of the explanation provided here, please find the diagrams in the two files that have been attached.
As can be clearly seen from the diagram, PR and QS are the diameters of the circle and they intersect each other at the centre, O of the circle.
The angle these diameters make at the point of intersection O is 90 degrees.
If Margot joins the points P,Q,R and S which are on the circumference of the circle, then we will get a square with sides PQ, QR, RS and SP as shown in the second diagram.
Thus, the correct option is Option A.
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Answer:
- arc BF = 76°
- ∠M = 31°
- ∠BGE = 121°
- ∠MFB = 111°
Step-by-step explanation:
(a) ∠FBM is the complement of ∠FBC, so is ...
∠FBM = 90° -52° = 38°
The measure of arc BF is twice this angle, so is ...
arc BF = 2∠FBM = 2(38°)
arc BF = 76°
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(b) ∠M is half the difference between the measures of arcs BE and BF, so is ...
∠M = (1/2)(138° -76°) = 62°/2
∠M = 31°
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(c) arc FC is the supplement to arc BF, so has measure ...
arc FC = 180° -arc BF = 180° -76° = 104°
∠BGE is half the sum of arcs BE and FC, so is ...
∠BGE = (1/2)(arc BE +arc FC) = (138° +104°)/2
∠BGE = 121°
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(d) ∠MFB is the remaining angle in ∆MFB, so has measure ...
∠MFB = 180° -∠M -∠FBM = 180° -31° -38°
∠MFB = 111°
