Question

1. ( mangle2 = 10 + 2x ) and ( mangle1 = 4x - 10 ). find ( mangle1 ).
2. ( mangle1 = 1 + 4x ) and ( mangle2 = 3x + 5 ). find ( mangle ywx ).

Explanation:

Step1: Set up the equation for vertical angles

Since \( \angle1\) and \( \angle2\) are vertical angles, \(m\angle1 = m\angle2\).
So, \(10 + 2x=4x - 10\).

Step2: Solve for \(x\)

Subtract \(2x\) from both sides:
\(10=4x - 2x-10\),
\(10 = 2x-10\).
Add \(10\) to both sides:
\(10 + 10=2x\),
\(20 = 2x\).
Divide both sides by \(2\):
\(x = 10\).

Step3: Find \(m\angle1\)

Substitute \(x = 10\) into \(m\angle1=4x - 10\).
\(m\angle1=4\times10 - 10\),
\(m\angle1=40 - 10\),
\(m\angle1 = 30\).

Answer:

\(m\angle1 = 30\)