Estude! Com Prof. Caju

Problema Proposto
1 - A diferença entre as medidas dos ângulos
consecutivos AOB e BOC é 30^o. Calcular
a medida do ângulo que formam 0B e a bissetriz do ângulo AOC.

[tex3]\mathsf{
\angle BOC(\theta) - \angle AOB(\alpha) = 30^o\implies \theta =30^o +\alpha(I)\\
Bissetriz: ~\angle AOF= \angle FOC\implies \frac{\alpha+\theta}{2}\\
\angle BOF = \theta - \angle FOC = \theta - \frac{(\alpha+\theta)}{2}=\frac{\theta-\alpha}{2}\\
De(I):\angle BOF = \frac{30+\alpha-\alpha}{2}=\boxed{\color{red}15^o}

}[/tex3]

Código: Selecionar tudoSHIFT+Click na eq = ZOOM

[tex3]\mathsf{
\angle BOC(\theta) - \angle AOB(\alpha) = 30^o\implies \theta =30^o +\alpha(I)\\
Bissetriz: ~\angle AOF= \angle FOC\implies \frac{\alpha+\theta}{2}\\
\angle BOF = \theta - \angle FOC = \theta - \frac{(\alpha+\theta)}{2}=\frac{\theta-\alpha}{2}\\
De(I):\angle BOF = \frac{30+\alpha-\alpha}{2}=\boxed{\color{red}15^o}

}[/tex3]