Question

for questions 6 - 9, the line drawn is an angle bisector of the triangle.
6.
find ( x ) if ( mangle 2 = 4x - 3 ) and ( mangle 1 = 3x + 5 ).
7.
( mangle 1=-1 + 6x ) and ( mangle 2 = 5x + 5 ).
find ( mangle 2 ).

Explanation:

Step1: Use the angle - bisector property

Since the line is an angle bisector, \(m\angle1 = m\angle2\).

Step2: Set up the equation for Question 6

For Question 6, we have \(3x + 5=4x−3\).
Subtract \(3x\) from both sides: \(3x+5 - 3x=4x - 3-3x\), which gives \(5=x - 3\).
Add 3 to both sides: \(5 + 3=x-3 + 3\), so \(x = 8\).

Step3: Set up the equation for Question 7

For Question 7, since \(m\angle1=m\angle2\), we have \(-1 + 6x=5x + 5\).
Subtract \(5x\) from both sides: \(-1+6x-5x=5x + 5-5x\), which gives \(x-1=5\).
Add 1 to both sides: \(x-1 + 1=5+1\), so \(x = 6\).

Step4: Find \(m\angle2\) for Question 7

Substitute \(x = 6\) into the formula for \(m\angle2\). \(m\angle2=5x+5\).
\(m\angle2=5\times6 + 5=30 + 5=35\).

Answer:

For Question 6: \(x = 8\)
For Question 7: \(m\angle2 = 35\)