Question

**#14.) which of the following statements will not prove ( l parallel m )?
i. ( angle 5 cong angle 2 )
ii. ( angle 4+angle 5 = 180^{circ} )
iii. ( angle 1+angle 7 = 180^{circ} )
iv. ( angle 8 cong angle 6 )
a.) i only
b.) ii only
c.) i and iii
d.) ii and iv
**#15.) spiral of old content: in the figure, ( angle axe ) is a straight angle, and ( angle axc ) is bisected by ( overrightarrow{xb} ). if ( mangle bxc=(8x - 30)^{circ} ) and ( mangle axb=(4x + 10)^{circ} ), find ( mangle bxe ).
a.) ( 10^{circ} )
b.) ( 130^{circ} )
c.) ( 50^{circ} )
d.) ( 40^{circ} )

Explanation:

Step1: Use angle - bisector property

Since \(\overrightarrow{XB}\) bisects \(\angle AXC\), then \(m\angle AXB=m\angle BXC\).
Set up the equation \(4x + 10=8x-30\).

Step2: Solve the equation for \(x\)

Subtract \(4x\) from both sides: \(10 = 4x-30\).
Add \(30\) to both sides: \(40=4x\).
Divide both sides by \(4\): \(x = 10\).

Step3: Find \(m\angle AXB\)

Substitute \(x = 10\) into \(m\angle AXB=(4x + 10)^{\circ}\), so \(m\angle AXB=(4\times10 + 10)^{\circ}=50^{\circ}\).

Step4: Find \(m\angle BXE\)

Since \(\angle AXE\) is a straight angle (\(m\angle AXE = 180^{\circ}\)), and \(m\angle BXE=m\angle AXE - m\angle AXB\).
Substitute \(m\angle AXB = 50^{\circ}\) and \(m\angle AXE=180^{\circ}\), we get \(m\angle BXE=180^{\circ}-50^{\circ}=130^{\circ}\).

Answer:

b. \(130^{\circ}\)