Question

Ajutir!Dau 50 de pct si coroana!​

Answer 1

Explicație pas cu pas:

sunt unghiuri în jurul unui punct

a)

$\measuredangle A_{0}OA_{1} + \measuredangle A_{1}OA_{2} + ... + \measuredangle A_{n-1}OA_{n} + \measuredangle A_{n}OA_{0} = 360 \degree$

$1\degree + 2\degree + ... + n\degree + \measuredangle A_{n}OA_{0} = 360 \degree$

$\dfrac{n\degree(n\degree + 1)}{2} < 360 \degree \iff n\degree(n\degree + 1) < 720 \degree$

$\implies valoarea \ \ maxim \breve a : \ \ n\degree = 26\degree$

(26×27=702; 27×28=756)

b)

$\measuredangle A_{5}OA_{14} = \measuredangle A_{5}OA_{6} + \measuredangle A_{6}OA_{7} + ... + \measuredangle A_{13}OA_{14} =$

$= 6\degree + 7\degree + ... + 14\degree = \dfrac{(6\degree + 14\degree) \cdot 9}{2} = \dfrac{20\degree \cdot 9}{2}$

$= \dfrac{180\degree}{2} = 90\degree$

$\implies \measuredangle A_{5}OA_{14} \ \ este \ \ unghi \ \ \bf drept$

c)

$\measuredangle A_{18}OA_{26} = \measuredangle A_{18}OA_{19} + \measuredangle A_{19}OA_{20} + ... + \measuredangle A_{25}OA_{26} =$

$= 19\degree + 20\degree + ... + 26\degree = \dfrac{(19\degree + 26\degree) \cdot 8}{2} = \dfrac{45\degree \cdot 8}{2}$

$= \dfrac{360\degree}{2} = 180\degree$

$\implies \measuredangle A_{18}OA_{26} \ \ este \ \ unghi \ \ \bf alungit$

q.e.d.