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kratose
16.04.2021 •
Mathematics
PLS HELP!! /BRAINLIST (DONT PUT AN RANDOM ANSWER) PLS HELP ASAP also if u just put anything I'll report you
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Ответ:
a) ∡AOC = 140 °
∡AOD = 40 °
b) ∡AOB = ∡BOC + ∡AOC și ∡BOC = ∡AOC (unghiuri formate din segmentul OC) prin urmare, segmentul OC bisectează ∡AOB
Step-by-step explanation:
a) Calculați măsurile unghiurilor ∢AOC și ∢AOD.
b) Arătați că jumătatea liniei opuse jumătății liniei OC este bisectoarea unghiului ∢AOB
a) Parametrii dați sunt;
∡AOC. ∡BOC. ∡COD și ∡DOA sunt unghiuri în jurul circumferinței unui cerc
∡AOB = 80 ° și ∡BOC = 140 °, segmentul CO este perpendicular pe segmentul DO
Prin urmare, avem;
∡AOB + ∡BOC + ∡AOC = 360 ° (Suma unghiurilor într-un punct = 360 °)
∴ ∡AOC = 360 ° - (∡AOB + ∡BOC) = 360 ° - (80 ° + 140 °) = 140 °
∡AOC = 140 °
∡BOC + ∡BOD = 180 ° (Suma unghiurilor unui triunghi = 180 °)
∡BOD = 180 ° - ∡BOC = 180 ° - 140 ° = 40 °
∡BOD = 40 °
∡ BOD + ∡AOD = ∡AOB
∡AOD = ∡AOB - ∡BOD = 80 ° - 40 ° = 40 °
∡AOD = 40 °
b) Deoarece avem ∡AOB = ∡BOC + ∡AOC și ∡BOC = ∡AOC = 140 °, avem;
∡AOB = 140 ° + 140 ° = 280 ° = 2 × ∡BOC = 2 × ∡AOC
Prin urmare, segmentul OC bisectează ∡AOB