Question

exercitiu 14 pag 146 (re upload)
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Answer 1

Explicație pas cu pas:

a)

$\angle A_{4}OA_{5} = \angle A_{5}OA_{6} = 2x \degree$

$9x \degree + 90 \degree = 360 \degree$

$9x \degree = 270 \degree$

$x \degree = 30 \degree$

$\angle A_{2}OA_{3} = x \degree \implies \angle A_{2}OA_{3} = 30 \degree$

$\angle A_{4}OA_{5} = 2x \degree \implies \angle A_{4}OA_{5} = 60 \degree$

$\angle A_{1}OA_{5} = 90 \degree + 4x \degree = 90 \degree + 120 \degree \\ \implies \angle A_{1}OA_{5} = 210 \degree$

b)

$\angle A_{6}OA_{2} = \angle A_{6}OA_{7} + \angle A_{7}OA_{8} + \angle A_{8}OA_{1} + \angle A_{1}OA_{2} = 30 \degree + 30 \degree + 30 \degree + 90 \degree = 180 \degree$

$\angle A_{7}OA_{3} = \angle A_{7}OA_{8} + \angle A_{8}OA_{1} + \angle A_{1}OA_{2} + \angle A_{2}OA_{3} = 30 \degree + 30 \degree + 90 \degree + 30 \degree = 180 \degree$

$\angle A_{8}OA_{4} = \angle A_{8}OA_{1} + \angle A_{1}OA_{2} + \angle A_{2}OA_{3} + \angle A_{3}OA_{4} = 30 \degree + 90 \degree + 30 \degree + 30 \degree = 180 \degree$