Question

find ( mangle acb ) if ( mangle 2 = 2x + 8 ) and ( mangle acb = 5x + 10 ).

Explanation:

Step1: Use angle - bisector property

Since \(CP\) is an angle - bisector of \(\angle ACB\), then \(\angle ACB = 2\angle2\).
So, \(5x + 10=2(2x + 8)\).

Step2: Solve the equation for \(x\)

Expand the right - hand side: \(5x + 10 = 4x+16\).
Subtract \(4x\) from both sides: \(5x-4x+10=4x - 4x+16\), which gives \(x+10 = 16\).
Subtract \(10\) from both sides: \(x=16 - 10=6\).

Step3: Find \(m\angle ACB\)

Substitute \(x = 6\) into the formula for \(m\angle ACB\).
\(m\angle ACB=5x + 10\), so \(m\angle ACB=5\times6+10\).
Calculate \(5\times6+10=30 + 10=40\).

Answer:

\(40\)