Question

1. * $overline{bf}perpoverline{ac}$ $angle fbc:$ ______ $angle ebf:$ ____ $angle abc:$ ______ acute, right, acute acute, straight, obtuse right, acute, obtuse right, obtuse, straight clear all unanswered

Explanation:

Step1: Recall angle - type definitions

A right - angle is 90 degrees, an acute angle is less than 90 degrees, an obtuse angle is between 90 and 180 degrees, and a straight angle is 180 degrees. Given that $\overrightarrow{BF}\perp\overrightarrow{AC}$, then $\angle FBC = 90^{\circ}$, so $\angle FBC$ is a right - angle.

Step2: Analyze $\angle EBF$

$\angle EBF$ is less than 90 degrees as it is part of the right - angle formed by $\overrightarrow{BF}$ and $\overrightarrow{AC}$, so $\angle EBF$ is an acute angle.

Step3: Analyze $\angle ABC$

$\angle ABC$ is greater than 90 degrees and less than 180 degrees, so $\angle ABC$ is an obtuse angle.

Answer:

right, acute, obtuse