Question

Repede vă rog, dau coroană!!!!!!​

Answer 1

Răspuns:

135°; 90°; 22,5°; 112,5°

Explicație pas cu pas:

ABCD este patrulater convex:

$\sphericalangle A + \sphericalangle B + \sphericalangle C + \sphericalangle D = 360 \degree$

$\sphericalangle B = \dfrac{2}{3} \cdot \sphericalangle A$

$\sphericalangle C = \dfrac{1}{6} \cdot \sphericalangle A$

$\sphericalangle D = 1 \dfrac{1}{4} \cdot \sphericalangle B = \dfrac{5}{4} \cdot \dfrac{2}{3} \cdot \sphericalangle A = \dfrac{5}{6} \cdot \sphericalangle A$

înlocuim în prima relație:

$\sphericalangle A + \dfrac{2}{3} \cdot \sphericalangle A + \dfrac{1}{6} \cdot \sphericalangle A + \dfrac{5}{6} \cdot \sphericalangle A = 360 \degree$

$6 \cdot \sphericalangle A + 4 \cdot \sphericalangle A + \sphericalangle A + 5 \cdot \sphericalangle A = 2160 \degree$

$16 \cdot \sphericalangle A = 2160 \degree \implies \sphericalangle A = 135 \degree$

$\sphericalangle B = \dfrac{2}{3} \cdot 135 \degree \implies \sphericalangle B = 90 \degree$

$\sphericalangle C = \dfrac{1}{6} \cdot 135 \degree \implies \sphericalangle C = 22.5 \degree$

$\sphericalangle D = \dfrac{5}{6} \cdot 135 \degree \implies \sphericalangle D = 112.5 \degree$