Question

Calculați măsurile unghiurilor patrulaterului convex ABCD stiind ca:
<B=2/3*<A
<C=1/6*<A
<D=5/4*<B

Answer 1

Răspuns:

<D=5/4•<B=5/4•2/3•<A=10/12•<A=5/6•<A

<A+<B+<C+<D=360°

<A+2/3•<A+1/6•<A+5/6•<A=360°

<A+2/3•<A+6/6•<A=360°

<A+2/3•<A+<A=360°

3<A/3+2<A/3+3<A/3=1080°/3

3<A+2<A+3<A=1080°

8<A=1080°

<A=135°

<B=2/3•A

<B=2/3•135=270/3=90°

<C=1/6•A=1/6•135=135/6=22,5°

<D=5/4•<B=5/4•90=450/4=112,5°