Question

1. \\(\overrightarrow{ab}\\) bisects \\(\angle cat\\). if \\(m\angle cat = 30^\circ\\) and \\(m\angle cab = (2x + 10)^\circ\\), then what is the value of \\(x\\)?

\\(x = 2.5\\)

Explanation:

Step1: Recall Angle Bisector Definition

An angle bisector divides an angle into two equal parts. So, \( m\angle CAB=\frac{1}{2}m\angle CAT \).

Step2: Substitute Given Values

We know \( m\angle CAT = 30^\circ \) and \( m\angle CAB=(2x + 10)^\circ \). Substituting into the formula: \( 2x+10=\frac{1}{2}\times30 \).

Step3: Simplify and Solve for x

First, calculate \( \frac{1}{2}\times30 = 15 \). So the equation becomes \( 2x + 10 = 15 \). Subtract 10 from both sides: \( 2x=15 - 10=5 \). Then divide by 2: \( x=\frac{5}{2}=2.5 \).

Answer:

\( x = 2.5 \)