Question

$AQ$ is the bisector of $\angle$A in $△ABC.$ Find the value of $x$, if
$\angle BAC=(20x+80{)}^o$
$\angle QAC=(15x+5{)}^o$

• A. $6^o$
• B. $7^o$
• C. $8^o$
• D. none

Answer 1

The correct option is B $7^o$

$\angle BAC=\angle BAQ+\angle QAC=2\angle BAQ=2\angle QAC$

$\angle QAC=\frac{1}{2}\angle BAC$

$(15x+5{)}^o=\frac{1}{2}(20x+80{)}^o$

$(15x+5{)}^o=(10x+40{)}^o$

$5x={35}^o$

$\therefore x=7^o$